V
elocity changes can be large and small. This ice climber is slowly climbing the
frozen waterfall. The climber has periods of zero velocity as he deeply sets the
pick axe into the ice wall. Then, his velocity increases as he uses the pick axe to pull
himself up the waterfall. The small increase in velocity is followed by another period
of zero velocity as he sets the pick axe again, then a small increase in velocity as he
pulls himself up. This process is repeated over and over as he slowly moves up the
frozen waterfall. In this chapter, you will learn more about velocity changes and how
to do calculations involving velocity changes.
236
MHR•Unit 3Motion
NS Science 10 CH6.indd 236
12/3/11 3:09:29 PM
LAUNCH ACTIVITY 6
How Can Velocity Change?
Whenyouwalkduringtheday,yourmotionchanges.
Youmightwalkfast,slowdown,andthenstop.Yougo
throughthesemotionswithoutthinkingaboutthem.The
position-timegraphbelowshowsthemotionofaperson
walkingalonga6mpathtowardagarden.
Position (m[toward garden])
Position vs. Time
2.Examinethegraph.Decidewhattypeofmotion
occursduringeach5secondinterval.
3.Trytowalkandduplicatethemotionthatisshown
inthegraph.Haveapartnertimeyourwalkwitha
stopwatch.
4.Switchrolesandhaveyourpartnerduplicatethe
motionwhileyoutimethemotion.
6
5.Compareyourmotionwithanothergroup.
Questions
4
1.Whichpartofthegraphdothemaskingtapemarks
represent?
2
0
2.Duringwhichtimeintervalsarethefollowing
motionsdescribed:
5
10
15 20
Time (s)
25
30
Materials
• metrestick
• maskingtape
• stopwatch
Procedure
1.Useametresticktomarka6mstraightpathinyour
classroomorotherspace.Placeamarkwithmasking
tapeat0m,3m,and6m.
(a)directionchange
(b)velocityincreases
(c)velocitydecreases
(d)velocityiszero
3.Ingeneral,whatistheslopeofthelineonthegraph
whenvelocityincreases,whenvelocitydecreases,
andwhenvelocitydoesnotchange?
4.Howdidyourmotioncomparewiththeothergroup?
Explainanydifferencesinmotion.
What You Will Learn
Why It Is Important
Inthischapter,youwill
• analyzegraphicallytherelationshipamong
velocity,time,displacement,andacceleration
• useformulasrelatingtodistance,speed,time,
displacement,velocity,andaccelerationto
calculateunknownquantities
Studyinggraphsdepictingmotiongivesyouabetter
understandingofhowthevariousfactorsinvolving
motion,suchasdisplacement,time,andvelocity,
arerelated.Scientistsoftenusemathematicsto
depictanddescribemotion.Learningtouseformulas
representingmotionallowsyoutoquicklyanalyze
motionwithoutdrawinggraphs.
Chapter 6AppliedMotion• MHR
NS Science 10 CH6.indd 237
237
12/3/11 3:09:32 PM
6.1 Changes in Velocity
What Do You Think?
•Howisthetermaccelerationusedineverydaylanguage?
•Thinkaboutasituationinwhichyouhavebeenonabicycleorinacar,truck,
train,boat,orairplane.Howdoyoufeel—whatdoesyourbodyexperience—as
thebicycleorothervehiclechangesspeedfromfastertoslowerandfromslower
tofaster?
Key Terms
acceleration
How would it feel to drive the race car shown in Figure 6.1? Some race
cars can go from a full stop to speeds of over 89 m/s (320 km/h) in less
than 4 s. Imagine how the driver is pressed back against the seat. Even
under normal driving conditions, you can feel a change in the motion of
the car when you speed up, brake rapidly, or turn quickly. However, when
a car is moving at a constant speed—uniform motion—you are almost
unaware of any motion at all. What is unique about changes in velocity
compared to constant velocity?
Figure 6.1 Imaginehowthisdriver
feelsastheracecarincreasesspeed
rapidly.
Describe how your body feels when
your motion changes from a complete
stop to moving in a forward direction.
Acceleration
acceleration, a a change
in the velocity of an object
during a time interval; rate
of change of velocity per
unit of time
238
Physicists define acceleration, a​
, as any change in the velocity of an object
during a time interval. The change might be an increase or decrease in
the magnitude of the velocity or a change in the direction of the object.
Because velocity is a vector quantity and acceleration is a change in
velocity, acceleration is also a vector quantity.
To explain why you feel a change in motion, or acceleration, think
about the cause of acceleration. Imagine an ice surface that is so smooth
that when a hockey puck slides across it, there is little friction. What
would speed up, slow down, or change the direction of the hockey puck?
You would have to hit it, or exert a force on it. When you feel a change in
the direction of a car in which you are riding, you are actually feeling the
force that is causing a change in the motion of your body. If no forces act
on an object in uniform motion, the motion will not change.
MHR•Unit 3Motion
NS Science 10 CH6.indd 238
12/3/11 3:09:34 PM
Graphing Accelerated Motion
How does a position-time graph of accelerated motion differ from a graph
of uniform motion? Examine the motion maps and graphs in
Figure 6.2 of sprinters on a high school track team speeding up and
slowing down. The time between images is 1 s. You can tell that the
sprinter in the graph in Figure 6.2A is speeding up because the distance
that the sprinter runs in 1 s becomes greater with each additional second.
The sprinter in the graph in Figure 6.2B is slowing down because the
distance travelled each second becomes shorter. Notice that the graphs are
both curved lines. When the speed increases, the graph curves upward.
When the speed decreases, the graph curves downward.
A
B
Position vs. Time
Figure 6.2 Whenanobjecthas
acceleratedmotion,themotionis
notuniform.Position-timegraphs
ofacceleratedmotionarealways
curved.
Explain how the motion maps
depict the changes in motion of the
sprinters.
Position vs. Time
Position (m[E])
d�
Position (m[E])
d�
Time (s)
t
Time (s)
The sprinter starts slowly, then
increases speed.
t
The sprinter starts rapidly, then
decreases speed.
Analyzing Graphs to Determine Zero Acceleration
By analyzing graphs of position versus time, you can determine whether
the velocity is zero, constant, or changing. You can learn even more from
a graph of velocity versus time, as shown in Figure 6.3. The position-time
graph in Figure 6.3A is a straight line, which indicates that the velocity is
constant. Similarly, a straight-line graph of velocity versus time, shown in
Position changes uniformly
Velocity is constant
Figure 6.3B, shows that the acceleration is constant. Because the change
in velocity is zero, the acceleration is also zero.
BB
Position vs. Time
Position (m[E])
d�
v�
Velocity vs. Time
Velocity (m/s[E])
AA
Time (s)
Position changes uniformly
t
Time (s)
Velocity is constant
t
Figure 6.3 Theslopeofthelinein
theposition-timegraph(A)shows
thatthevelocityisconstant.The
slopeofthevelocity-timegraph
(B)alsoindicatesthatvelocityis
constant;therefore,accelerationis
alsoconstant.Thezeroslopeofthe
velocity-graphindicatesthatthe
accelerationiszero.
Identify the key factor in each
of these graphs that indicates
that velocity and acceleration are
constant.
Chapter 6AppliedMotion• MHR
NS Science 10 CH6.indd 239
239
12/3/11 3:09:36 PM
Analyzing Graphs To Determine Positive Acceleration
In Figure 6.4A, the position-time graph is a curve, which indicates that
the velocity is increasing. Earlier, you learned that a straight-line in a
position-time graph represents constant velocity. If you look at Figure
6.4B, you can see that velocity increases uniformly. When velocity
increases uniformly, as shown in Figure 6.4B, the acceleration is constant.
In this example, the velocity is increasing and the acceleration is positive,
which is indicated by the positive slope of the velocity-time graph.
AA
BB
Position vs. Time
v�
Velocity vs. Time
Velocity (m/s[E])
d�
Position (m[E])
Figure 6.4 Thecurveofthepositiontimegraph(A)indicatesthatthe
velocityisincreasing.Theslopeofthe
velocity-timegraph(B)indicatesthat
velocityisincreasingandisconstant.
Accelerationisalsouniformand
positive.
Explain what you look for in a
position-time graph to determine if
velocity is increasing.
Time (s)
t
Position-Time graph curves upward
Time (s)
t
Velocity increases uniformly
Analyzing Graphs To Determine Negative Acceleration
In Figure 6.5A, the position-time graph curves in a downward direction.
This direction is opposite to that of the curve in Figure 6.4A. The
downward curve once again indicates that the velocity is changing.
However, the direction of the curve means that the magnitude of the
velocity is decreasing, as shown in the velocity-time graph in
Figure 6.5B. The velocity-time graph shows that the velocity is
decreasing uniformly, again indicating that the acceleration is constant.
Because the velocity is decreasing, the acceleration is negative, which is
indicated by the negative slope of the velocity-time graph. You might have
heard the term deceleration. Deceleration is not a scientific term. The
correct term for decreasing acceleration is negative​acceleration.
Complete Activity 6-1A, Accelerated Motion, on the next page to
learn more about acceleration.
d�
BB
Position vs. Time
Time (s)
t
Position-Time graph curves downward
240
v�
Velocity vs. Time
Velocity (m/s[E])
AA
Position (m[E])
Figure 6.5 Thecurveofthepositiontimegraph(A)showsthatthe
velocityisdecreasing.Theslopeofthe
velocity-timegraph(B)indicatesthat
velocityisdecreasingandisconstant.
Accelerationisalsoconstantand
negative.
Explain what you look for in a
position-time graph to determine if
velocity is decreasing.
Time (s)
t
Velocity decreases uniformly
MHR•Unit 3Motion
NS Science 10 CH6.indd 240
12/3/11 3:09:38 PM
F i nd Out ACTIV ITY
6-1A Accelerated Motion
Withafewpiecesofequipment,youcananalyze
acceleratedmotion.
Materials
•
•
•
•
•
•
•
•
labtable
severalbooksorotherflatobjects
C-clamp
recordingtimerorelectronicsparktimer(60cycles/
second)
tickertapeorsparktape
maskingtape
dynamicscart
ruler
3.UsetheC-clamptofastenarecordingtimertothe
raisedendofthetable.Cutapieceoftickertape1m
long.Insertthetickertapeintothetimer,andusethe
maskingtapetoattachthetickertapetothebackof
thedynamicscart.
4.Holdthedynamicscartstationarynexttothetimer
andreleaseitafterthetimeristurnedon.Havea
partnercatchthecartbeforeitfallsoffthetable.
5.Drawalinethroughthefirstdotonthetapeand
labelitt0.0s.Countsixdotsfromthet0.0s
line,anddrawanotherlinethroughthesixthdot.
Labelthislinet0.1s.Measurethedistance
betweenthesetwolines,andrecordthisvalueinthe
tableasthedisplacementduringthetimeinterval
t0.0tot0.1s.
t = 0.0 s t = 0.1 s
t = 0.2 s
t = 0.3 s
Anexampleofhowtomarkthetickertape
6.Fromthet0.1sline,drawalinethroughthesixth
dot.Labelthislinet0.2s.Measurethedistance
betweenthet0.1slineandthet0.2sline.
Recordthisvalueasthedisplacementduringthetime
intervalt0.1tot0.2s.
Steps 2 and 3
Steps2and3
What to Do
1.Copythefollowingdatatableintoyournotebook.
Givethetableatitle.
Time
Interval (s)
Displacement
(cm)
Average
Velocity
(cm/s[forward])
0.0to0.1
0.1to0.2
0.2to0.3
0.3to0.4
0.4to0.5
0.5to0.6
0.6to0.7
0.7to0.8
2.Raiseoneendofalabtable10cmto15cmby
placingseveralbooksorotherflatobjectsunderthe
backlegs,asshowninthediagram.
7.Continuemeasuringandrecordingthedisplacements
foreachofthetimeintervalsinyourdatatable.

___
d

ave calculatetheaverage
8.Usingtheequationv
t
velocityforeachofthe0.1stimeintervals.Record
thesevaluesinyourdatatable.
9.Cleanupandputawaytheequipmentyouhave
used.
What Did You Find Out?
1.Useasentencetodescribehowthespacingofthe
dotsfortheacceleratedmotionisdifferentfromthe
spacingofthedotsyouwouldexpectforuniform
motion.
2.Useyourdatatocreateaposition-timegraph.
Howdidthedisplacementofthecartchangeforeach
ofthe0.1stimeintervals?
3.Useyourdatatocreateavelocity-timegraph.
Howdidtheaveragevelocityofthecartchangefor
eachofthe0.1stimeintervals?
Chapter 6AppliedMotion• MHR
NS Science 10 CH6.indd 241
241
12/3/11 3:09:41 PM
Check Your Understanding
1. Describe the velocity-time graph of an object with zero
acceleration, positive acceleration, and negative acceleration.
2. Compare and contrast deceleration and negative acceleration.
3. Is acceleration a vector or scalar? Explain your answer.
4. Describe a scenario in which an object has positive acceleration.
5. Describe a scenario in which an object has negative acceleration.
6. Describe a scenario in which an object has zero acceleration.
Calculating Displacement Graphically
You have learned that a velocity-time graph yields information about
the acceleration of an object. A velocity-time graph also yields useful
information about the displacement of the object. The​displacement​of​an​
object​from​time,​t1,​to​time,​t2,​is​equal​to​the​area​under​the​velocity-graph​
during​the​defined​time​interval.
The Sample Problem below shows you how to use a velocity-time
graph to calculate displacement. Use the Practice Problems that follow to
practice using this method for calculating displacement.
Sample Problem: Calculating Displacement Using a
Velocity-Time Graph
Problem
A driver travelling near Kejimkujik National Park at a velocity of
14 m/s[S] sees a bobcat in the road. It takes the driver 0.50 s to
react, then the driver steps on the brake to stop the car. From the
time the driver saw the bobcat to the time that the car stopped is
3.0 s. Use a velocity-time graph to determine the displacement of
the car during that 3.0 s.
What Is Required?
You must calculate the displacement using a velocity-time graph.
What Is Given?
You know the initial velocity is 14 m/s[S].
You know the reaction time is 0.5 s.
You know the total time interval is 3.0 s.
Plan Your Strategy
Draw a velocity-time graph. Calculate the area under the graph
between 0.0 s and 3.0 s.
continued on next page
242
MHR•Unit 3Motion
NS Science 10 CH6.indd 242
12/3/11 3:09:41 PM
Velocity vs. Time
Sample Problem: Calculating Displacement Using a
Velocity-Time Graph—continued
Draw the velocity-time graph, as shown on the right.
The area on the graph that is shaded in red is a rectangle. In
order to find the length and width of the rectangle, you read the
measurements from the x-axis and the y-axis. The calculation is
shown below:
area  length × width
m[S]
× (0.50 s)  7.0 m[S]
 14.0 ____
s
(
)
Next, you must calculate the area of the triangle—the part of the
graph that is shaded in blue. Again, you read the values that you
need for the formula from the axes on the graph. The calculation
for the area of the triangle is shown below:
1 × base × height
area  __
2
m[S]
1 (2.5 s) 14.0 ____
 __
 17.5 m[S]
s
2
​
(
)
Now, you must add the two displacements together, and then you
must round off the answer to the correct number of significant
digits.
​
​
d​
​  7.0 m[S]  17.5 m[S]  24.5 m[S]  25 m[S]
12.0
Velocity (m/s[S])
Act on Your Strategy
14.0
10.0
8.0
6.0
4.0
2.0
0
0.5 1.0 1.5 2.0 2.5 3.0
Time (s)
Problem Tip
Theshapeunderthegraphisan
awkwardshape,butitcanbe
dividedintotwostandard-size
pieces.Theareasofthetwopieces
canbeaddedtogivethetotal
areaunderthegraph.
The total displacement of the car during that 3.0 s time interval
was about 25 m[S].
Practice Problems
1. A driver was travelling from Chelsea to Waterloo at a constant
velocity of 16 m/s[E] over a 30.0 s time interval. What was
the driver’s displacement during this time interval?
2. A train is travelling to Halifax. As the train is approaching the
station, it slows from 12 m/s[E] to 0 m/s in 90.0 s. What
was the train’s displacement during the 90.0 s time interval?
3. A park employee used a snowmobile in Cape Breton
Highlands National Park to reach a hiker who had become
stranded. During part of the trip, the employee travelled a
constant velocity of 8.5 m/s[N] for 30.0 s. The employee
then spotted the stranded hiker and continued travelling
north, but came to a stop over the next 60.0 s. What is the
park employee’s displacement over the 90.0 s time interval?
Chapter 6AppliedMotion• MHR
NS Science 10 CH6.indd 243
243
12/3/11 3:09:43 PM
Motion in a Car
Suggested Activity
ConductanInvestigation6-1B
TheDirectionofAcceleration
Every time you ride in a car or on a bus, you feel the affects of
acceleration on your body. The physics involved in the situations below
can be complex. The forces involved are simplified in the descriptions
below.
Zero Acceleration in a Car
Imagine riding in a car on a flat, smooth highway at a constant velocity.
You sit comfortably in your seat and you do not feel any forces pushing
against you. Of course, there are forces acting on you, because the seat
is exerting an upward force on you that is opposing gravity. In this
example, you are experiencing the smooth ride of zero acceleration, as
demonstrated by the person in Figure 6.6A.
Positive Acceleration in a Car
Imagine riding in a car when a red light turns green. The driver gives
the car a lot of gas, and the car bolts forward. You feel the positive
acceleration of the car when the car seat pushes you forward. Although
you feel as though you are being pushed backward, the car seat is actually
pushing you forward.
Negative Acceleration in a Car
Now, imagine that you are riding in a car at highway speed and a
deer runs onto the road. The driver slams on the brakes. The car is
experiencing negative acceleration. You feel the affects of negative
acceleration when your body is restrained by the seat belt as you are
propelled forward. Your head and shoulders might experience whiplash as
the car finally comes to a stop. The crash dummy in Figure 6.6B is being
restrained by the seatbelt as the car undergoes negative acceleration.
A
B
Figure 6.6 Asmoothrideinwhichyoudon’tfeelanyforcesactingonyourbodyisoftenaresultofzeroacceleration(A).Whenthedriverslams
onthebrakes,yourbodyfeelsasthoughitisbeingthrownforwardintheseat(B).
Describe what it feels like on your body when a car is accelerating quickly.
244
MHR•Unit 3Motion
NS Science 10 CH6.indd 244
12/3/11 3:09:47 PM
6-1B The Direction of Acceleration
SkillCheck
•Observing
•Measuring
•ControllingVariables
•EvaluatingInformation
Conduct an InVesTIgATIOn
Weusuallydefineforwardmotionofanobjectaspositive().Ifanobject
increasesitsforwardvelocity,theaccelerationwouldalsobepositive(),which
meansitisacceleratingforward.Iftheobjectslowsdownitsforwardmotion,then
theaccelerationisbackwardornegative().Inthisinvestigation,youwillanalyze
accelerationbycomparingaveragevelocityduringequaltimeintervals.Remember,
forequaltimeintervals,greaterdisplacementsrepresentgreateraveragevelocity.
Question
Safety
Howisaccelerationrepresentedonamotionmapordiagramcreatedbya
recordingtimer?
Materials
• recordingtimerorelectronic
sparktimer(60cycles/
second)
• 2moftickertapeorspark
tape
• C-clamp
Anexampleofhowtomarkthetickertape
Procedure
1.UsetheC-clamptofastenthetimertotheendofthetable.Cuta2mlengthof
tickertapeandinsertitintotherecordingtimer.
2.Turnontherecordingtimer,andpullapproximately1.5mofthetapethrough
thetimerwithnon-uniformmotion.Makesurethatthespeedyoupullthetape
increasesanddecreasesseveraltimesduringthetimeyouarepulling.
3.Turnoffthetimer.
4.Usingapencil,drawalinethroughthefirstdotonthetape.
5.Drawalinethrougheverysixthdotallthewayalongthetape.
6.Makeasketchofthetickertapeinyournotebook.
7.Cleanupandputawaytheequipmentyouhaveused.
Analyze
1.Thedisplacementforeachoftheseequaltimeintervalsisproportionaltothe
averagevelocitythatthetapewasbeingpulled.Iftheintervaldistanceis
increasing,thentheaveragevelocityofthetapeisincreasing.Thisindicates
thetapeisacceleratinginthedirectionofmotion.Iftheintervaldistance
isdecreasing,thentheaveragevelocityofthetapeisalsodecreasing.This
indicateseitherthetapeisacceleratingorthedirectionoftheaccelerationis
oppositethedirectionofthevelocity.Drawanarrowindicatingthedirectionof
theaccelerationforsuccessivetimeintervals.
Conclude and Apply
1.Explainwhysomeoftheaccelerationarrowspointindifferentdirections.
2.Turnyourtickertapesoitisbackward.Analyzetheaccelerationarrowsthatyou
havemarkedonyourtape.Aretheystillcorrect?Explain.
Chapter 6AppliedMotion• MHR
NS Science 10 CH6.indd 245
245
12/3/11 3:09:50 PM
Human Acceleration
Inthelate1940s,therewasanincreasingemphasison
speedintransportation.Refinementstothedesignofthe
jetplanehadallowedittoreachspeedsofmorethan
700km/h.GrandPrixracecarsweretravellingatmore
than150km/h.However,thefasterspeedscamewitha
hugecost:crashesatthesespeedswereusuallyfataldue
tothelargeaccelerationexperiencedbypilots,drivers,
andpassengers.
mountedbackward.Aftertheveryuncomfortable
acceleration,nomeasurementswererecordedduetothe
backwardsensors,makingStapp’seffortwasted.Infuture
experiments,Stappwasfamousforalwaystryingto
considereverythingthatcouldpossiblygowrongbefore
undertakingtheexperiment.
ColonelJohnStapp(1910–1999)wasapioneerin
studyingtheeffectsofaccelerationonthehumanbody.
Hewascalled“thefastestmanonEarth.”Colonel
StappdidmostofhisresearchatEdwardsAirForce
Base,inCalifornia,wherehewasstationedasamedical
doctor.Backin1947,scientistsdidnothavecomputers
andcomplexcrash-testdummiestouseinanalyzing
accelerationsonhumans.Todohisresearch,Stapp
subjectedhimselftolargeaccelerations.Accelerationof
1g(gisthesymbolforthevalueoftheaccelerationdue
togravity)isequivalenttotheaccelerationofanobject
droppednearthesurfaceofEarth.Itwasbelievedthatan
accelerationofmorethan18g(176m/s2)wouldcause
death,butStappexperiencedupto46g(451m/s2)and
survived.
TheresultsofJohnStapp’sresearchareevidentin
today’ssafetyfeatures.Stappwasdedicatedtosafetyand
tookeveryopportunitytosupporttheuseofsafetybelts
incars.Thelapbeltsandshoulderstrapsincarstodayare
aresultofStapp’sresearch.Stappalsodiscoveredthat
humanscanwithstandalargeraccelerationwhenriding
backwardthanwhenridingforward.Thisfindinghasled
toinfantseatsbeingpositionedfacingbackwardinthe
rearseatsofcars.
JohnStappevenmadeanimpactonourlanguage.
YoumayhaveheardofMurphy’slaw,whichstates“If
anythingcangowrong,itwill.”Murphywasatest
engineerworkingwithStapponhisexperiments.
Inoneofthefirstridesonthe“humandecelerator,”
Stappwasfittedwith16accelerometersplacedon
variouspartsofhisbody.Unfortunately,all16were
246
The“humandecelerator”consistedof610mofrailwaytrack
stretchingacrosstheairbase.Rocketspropelledthe680kg
carriage.Oncethecarriagewasmovingfastenough,a14mlong
brakingsystem,themostpowerfuleverconstructed,wascontrolled
tostopthepassengerwithacalculatedacceleration.
Questions
1. WhatwasthepurposeofJohnStapp’sresearch?
2. WhatmaximumaccelerationdidJohnStapp
withstand?
3. WhatmodernsafetyfeaturesresultedfromJohn
Stapp’sresearch?
MHR•Unit 3Motion
NS Science 10 CH6.indd 246
12/3/11 3:09:57 PM
Checking Concepts
1. Use words and a sketch to describe the
appearance of a velocity-time graph if uniform
acceleration is occurring.
2. On the following velocity-time graph, indicate
the intervals where the acceleration is positive
and where the acceleration is negative.
Velocity (m/s[E])
Velocity vs. Time
80
60
40
20
0
5
10
15 20
Time (s)
25
30
3. In the graph from question 2, explain what is
occurring during the time interval from 15 s
to 20 s.
4. A truck travels a displacement of 100 km[N]
at an average velocity of 55 km/h[N]. Is it
possible that acceleration occurred during
the time interval when this displacement
occurred? Explain your answer.
5. A piece of ticker tape was attached to a
dynamics cart and the cart moved up and
down a series of ramps. One segment of the
ticker tape was analyzed and it was found
that the dots were getting closer together
over the time interval. What does this
observation indicate was occurring during the
time interval for this segment of ticker tape?
Explain your answer.
Understanding Key Ideas
6. A car is travelling in reverse when the driver
presses the brakes. If the forward direction is
chosen to be positive, would the acceleration
during braking at a red light be positive or
negative? Explain your answer.
7. A train is travelling at 15 m/s[S] for
20.0 s before it slows from 15m/s[S] to a
stop 90.0 s later. During this time interval of
110.0 s, what is the total displacement of the
train?
8. Explain how a velocity-time graph can be
used to determine the displacement of the
object described by the graph over a time
interval.
9. On a drive from Jeddore to Sheet Harbour,
Richard maintained a constant velocity of
21.0 m/s[E] for a 45.0 second interval of
time. What was the total displacement during
this time interval?
10. A car is racing around a banked oval racetrack
at a constant speed of 150 km/h. On the
first straightaway, the car is travelling north.
Indicate the type of acceleration that occurs
at each of the following points:
(a) the midpoint of the first turn
(b) the midpoint of the back straightaway
(c) the midpoint of the last turn
11. Draw a velocity-time graph for a ball that has
been rolled up a ramp that is long enough to
allow for the ball to stop and then roll back
down to where it started. The velocity of the
ball is 5 m/s[up the ramp] when it was first
released. (Hint: Use [up the ramp] as the
positive direction. The acceleration of the ball
is 9.8 m/s2.)
12. Use your graph from question 11 to answer
the following questions:
(a) Determine the total displacement of the
ball from t  0 s to t  1 s.
(b) Determine the total displacement of the
ball from t  1 s to t  2 s.
(c) Explain how the results from parts (a) and
(b) can be used to justify the fact that, at
the end of the 2 s time interval, the ball
returns back to the point from which it
was released.
Project Prep
Arethereanywaystoincorporatewhatyou
havelearnedinthissectionintoyourproject
attheendofthisunit?Discussyourideaswith
yourclassmates.
Chapter 6AppliedMotion• MHR
NS Science 10 CH6.indd 247
247
12/3/11 3:09:59 PM
6.2 Using Motion Formulas
What Do You Think?
•Whatvariableswouldyouusetodeterminethespeedofanobject,andhow
wouldyouarrangethemintheformofamathematicalformula?
•Nameatleasttwosituationsinwhichbeingabletocalculatethevelocityofan
objectwouldbeuseful,andexplainwhyitwouldbeuseful.
•Whydoyouthinkthatitisimportanttokeeptrackoftheandsignsof
speed,velocity,andacceleration?
By re-examining the concepts of distance and displacement, you can
develop a clear understanding of how to calculate speed and velocity.
Examine the map in Figure 6.7.
Moncton
N
Petitcodiac
Amherst
Oxford
Springhill
Truro
Parrsboro
N40°E
displacement = 153 km
Brockfield
distance = 391 km
Middleton
Bridgetown
Kentville
Milville
Windsor
Stewiacke
Enfield
Fall River
E
Annapolis
Royal
Mahone Bay
Bridgewater
Halifax
Lunenburg
Figure 6.7 Distanceanddisplacementoftenhavedifferentmagnitudes.
Explain why a person driving in a car cannot follow the displacement arrow to get to Amherst.
Calculating Speed and Velocity
The black arrow shows the displacement from Annapolis Royal to
Amherst. To avoid clutter on the map, no reference point is chosen and
position vectors are not included. The distance along the displacement
arrow is approximately 153 km. The direction that the arrow points is
about 40° east of north. That means that if you pointed an arrow north,
like the red arrow, and then rotated it through an angle of 40° toward
the east, you would be pointing in the direction of the displacement on
the map. You would describe the displacement from Annapolis Royal to
  153 km[N40°E].
Amherst as d​
248
MHR•Unit 3Motion
NS Science 10 CH6.indd 248
12/3/11 3:10:00 PM
Distance and Displacement
If you drove from Annapolis Royal to Amherst, you could not drive in a
straight line. You would follow the blue path on the map. The distance
along the blue path is approximately 391 km. This distance is completely
described by writing d  391 km. No direction is involved. Notice that
the distance is longer than the magnitude of the displacement. If you
compare the distance travelled on the highways to the displacement arrow,
it is easy to see why these two numbers differ so much.
Speed and Velocity Formulas
You read about speed and velocity in Chapter 5 and you know that they
have different definitions in science. Think of a weather report in which
the meteorologist is reporting wind velocities. Think of auto races in which
cars run at speeds of over 200 km/h. Recall that speed is a scalar and
velocity is a vector. Speed is related to distance, and velocity is related to
displacement. Both quantities involve time.
If you were going to determine a sprinter’s speed or velocity, you
would probably start a stopwatch the instant the sprinter left the starting
line. However, you might want to know how fast a certain sprinter was
running during the first half and last half of a race. Assume that the race is
a 50 m dash. You would start the stopwatch when the race started. Then
you would check your stopwatch when the sprinter reached the 25 m
line and again at the end of the race. You would have measured two time
intervals. Recall from Chapter 5 that the formula for a time interval is
t  tf  ti or t  t2  t1
Now you are ready to define speed and velocity mathematically.
Remember that speed is the distance travelled by an object during a given
time interval. Velocity is the displacement of an object during a time
interval divided by the time interval. The direction of the velocity is the
same as the direction of the displacement. Since the speed and velocity
might change during an interval of time, the formulas below represent
average speed and average velocity. The formulas look very similar, but an
example will reveal some slight differences.
Speed
d​​​
vave  ___
t
where vave is average speed in
metres per second, m/s
d is distance in metres, m
t is the time interval in
seconds, s
Velocity
  d​

d​

d​
2
1
v​
​​or vave  _______
ave  ___
t

t1
t
2
where v​
ave is average velocity in
metres per second, m/s
 is displacement in metres, m
d​
​
d​
​2 is the final position in
metres, m
​
​1 is the initial position in
d​
metres, m
t is the time interval in
seconds, s
​ t2 is the final time in seconds, s
​ t1 is the initial time in seconds, s
Chapter 6AppliedMotion• MHR
NS Science 10 CH6.indd 249
249
12/3/11 3:10:01 PM
Using Speed and Velocity Formulas
Imagine that your family drove from Annapolis Royal to Amherst. The
entire trip took 5.2 h. As you read previously, the distance along the
highway is 391 km and the displacement is 153 km[N40ºE]. You could
calculate the speed and velocity as shown below.
Speed
vave
vave
Velocity

d​
v​
​​
ave  ___
t
153 km [N40°E]
v​
ave  _______
5.2 h
km [N40°E]
v​
ave  29.423 ___
h
___
km
v​
[N40°E]
ave  29
h
d​​​
 ___
t
391 km
 _______
5.2 h
km
vave  75.192 ___
h
___
km
vave  75
h
Did You Know?
Tosolvemotionproblems,
youmayneedtomakeunit
conversions.Forexample,if
speedisgiveninkm/h,you
mightneedtoconvertto
m/s.Convertkm/htom/sby
multiplyingyourquantitybythe
ratioofmetrestokilometres
andbytheratioofhoursto
seconds.Toconvert55km/hto
m/s,dothefollowing:
(
)(
)(
Although the values for speed and velocity describe the same trip, they
look quite different. The reason for the difference lies in the definitions
of distance and displacement. Remember that displacement is always
measured along a straight line joining the initial and final positions.
Distance, however, is measured along the actual path taken. The time
intervals are the same.
The map from Figure 6.7 is repeated here so you can examine it
along with the calculations for speed and velocity shown above. Be sure
you understand why these magnitudes differ. Then work through the
Sample Problems on the next page, and complete the Practice Problems
that follow to improve your skills for solving problems that involve speed
and velocity.
Moncton
N
Petitcodiac
Oxford
Springhill
)
55km
1000m _____
1h ______
______
h
1km 3600s
(55)(1000)
_________
__
m
s 15.28m/s
3600
m
15__
s
Whenunitscancelproperly,you
knowyourequationiscorrect.
Amherst
N40°E
displacement = 153 km
Brockfield
distance = 391 km
Middleton
Bridgetown
Kentville
Milville
Windsor
Stewiacke
Enfield
Fall River
E
Annapolis
Royal
Mahone Bay
Bridgewater
250
Truro
Parrsboro
Halifax
Lunenburg
MHR•Unit 3Motion
NS Science 10 CH6.indd 250
12/3/11 3:10:02 PM
Sample Problem: Part A
Did You Know?
Problem
A car travelled a distance of 550 m in a time interval of 35 s.
What was the speed of the car?
What Is Required?
d​​​.
You must calculate the speed of the car, vave  ___
t
What Is Given?
You know the distance, d, is 550 m and the time interval,
t, is 35 s.
Plan Your Strategy
Your teacher may require you to draw a sketch as part of your
solution to this and other problems. However, here you will be
shown how to solve this problem without drawing a sketch. The
data given are time interval and distance. Therefore, use the
d​​​.
formula that involves distance and time interval, vave  ___
t
Act on Your Strategy
Place the known values in the formula and solve for the unknown.
d​​​ ______
550 m  15.714__
m  16__
m
vave  ___
s
s
35 s
t
The car was travelling at a speed of about 16 m/s.
Sample Problem: Part B
Measurement,communication,
andprecisionareessentialto
scienceandthemathematics
usedincalculationsfor
science.In1999,NASA’s
Mars Climate Orbiterspace
probedisappeared.Several
engineeringgroupshadworked
ontheprobe,whichcostmore
than$300milliontodesign,
construct,andlaunch.An
investigationlaterfoundthat
onegrouphadusedSIunits,
suchasmetresandkilograms.
Anothergrouphadassumed
thatdatawerebeingrecorded
infeet,inches,andpounds,
unitscommonlyusedinthe
UnitedStates.Asaresult,the
computersontheprobemade
errorsinthecalculationsfor
puttingtheprobeintoorbit.
Itprobablyburnedupinthe
Martianatmospherebecauseof
theseinaccuratecalculations.
Problem
Two trainers with stopwatches are timing a runner who is training
for a race. Both trainers start their stopwatches when the runner
leaves the starting point. The first trainer is standing at a position
that is 12 m[S] of the starting point and the second trainer is
standing at a position 65 m[S] of the starting point. Each trainer
stops her stopwatch when the runner passes her. The first trainer’s
stopwatch reads 1.6 s and the second trainer’s stopwatch reads
8.7 s. What was the athlete’s velocity while racing between the
trainers?
What Is Required?
  d
d​
2
1
athlete’s velocity between the trainers, v​
ave  _______
t2  t1
What Is Given?
d1  12 m[S]
​
​2  65 m[S]
d​
t1  1.6 s
t2  8.7 s
continued on next page
Chapter 6AppliedMotion• MHR
NS Science 10 CH6.indd 251
251
12/3/11 3:10:03 PM
Sample Problem: Part B—continued
Problem Tip
Plan Your Strategy
Carefullykeeptrackofyour
units.Ifyourunitsdonotcancel
correctlyoryouendupwith
thewrongunitsintheanswer,
youhaveincorrectlysetupthe
problem.Analyzingtheunitsas
youworktheproblemisone
waytocheckyourwork.
The problem gives the positions of the trainers. They stopped their
stopwatches when the runner was at those positions. The trainers
also started their stopwatches when the runner was at position zero.
Therefore, the readings on their stopwatches are the times that the
runner passed each position. Use the formula for velocity that
  d
d​
2
1
involves positions and times, v​
ave  _______
t2  t1 .
Act on Your Strategy
Place the know values in the formula and solve for the unknown.
d2  d1
65
m[S]  12 m[S]  ________
m[S]  7.3 __
53 m[S]  7.26_____
__________________
m
v​
​ ave  _______
s
s
t2  t1 
7.3 s
8.7 s  1.6 s
​
The athlete was running at a velocity of about 7.3 m/s[S].
Sample Problem: Part C
Problem
A trip to the grocery store takes 660 s with an average speed of
12.7 m/s. What is the distance to the store?
What Is Required?
You must rearrange the speed formula to calculate distance.
What Is Given?
average speed, vave  12.7 m/s and the time interval t  660 s.
Plan Your Strategy
d​​​.
The formula for calculating average speed is vave  ___
t
Multiply both sides of the equation by t to get the formula for
calculating the distance
d  vave  t.
Act on Your Strategy
Place the known values in the formula and solve for the unknown.
m  660 s  8382 m  8.4 km
d  vave  t​ 12.7__
s
The store is about 8.4 km away.
Practice Problems
4. A stunt cyclist goes 39 m in 3.0 s. How fast is the cyclist riding?
5. A skier goes 148 m[W] in 5.5 s. What is the skier’s velocity?
6. A jet plane travels a distance of 959 km from Ottawa, Ontario
to Halifax, Nova Scotia in 1 h and 28 min. Determine the
average speed of the jet plane in metres per second. (Hint:
There are 1000 m in 1 km, 60 s in 1 min, and 3600 s in 1 h.)
252
MHR•Unit 3Motion
NS Science 10 CH6.indd 252
12/3/11 3:10:03 PM
Practice Problems—continued
7. A cheetah runs at a velocity of 29 m/s[N]. If it runs for 8.4 s,
what is its displacement?
8. Imagine that you and your family are driving to a friend’s
home, which is 95 km away. If you drive at an average speed
of 85 km/h, how long will it take you to get there?
9. A 100 m track is marked off in metres. When a sprinter leaves
the starting line, timers are started. The sprinter passes the
12 m[E] mark at 1.8 s and passes the 56 m[E] mark at 6.7 s.
What was the sprinter’s average velocity between those two
positions?
10. The fence posts around a large pasture are 2.5 m apart. A
horse starts running west beside the fence. When the horse
passes the fifth fence post, the second hand on a watch is on
the 9.0 s mark. When the horse passes the 14th fence post, the
second hand is on 11.5 s. What is the horse’s average velocity?
11. Charlene plays on a hockey team that has chartered a bus
so that the team can play in a tournament elsewhere in the
province. At 2:15 p.m., the bus taking the team has travelled
35 km. Awhile later, at 3:09 p.m. the bus has travelled
116 km. What is the average velocity of the bus?
12. A cougar can leap 11 m horizontally. If it spends 1.8 s in the
air, what was its average speed?
13. If a maglev (magnetic levitation) train ran between Wedgeport
and Halifax, a distance of 295 km, it could make the trip in
about 0.75 h (three-quarters of an hour). What would be the
average speed of the maglev train?
14. A car and driver leave Big Lorraine at noon. The car passes
through Port Hawkesbury at 2:15 p.m. and reaches Sackville
at 5:45 p.m. Big Lorraine is 168 km from Port Hawkesbury
and Sackville is 290 km from Port Hawkesbury. What was the
average speed of the car between Big Lorraine and Sackville?
15. Caroline and Victoria are training their dog to carry messages
between the store where one sister works and the restaurant
where the other works. They want to find out how long it will
take the dog to make the trip. They measure the displacement
between the store and the restaurant and find that it is
1.2 km[W]. While training the dog, they time it with a
stopwatch and find the time to be 14 min. What was the dog’s
average velocity?
16. If you walk to school at a speed of 1.2 m/s and it takes you
18 min to reach the school, what is the distance from your
home to the school?
Problem Tip
Asyoureadtheproblem,note
theunitsthatareused.Dothe
calculationsforunitconversions
first.Then,allofyournumberswill
havethecorrectunitswhenyou
beginyourcalculations.
Did You Know?
AnewhighspeedtraininChina
travelsatspeedsbetween
250km/hand300km/h.The
traintravelsfromWuhan,China,
andGuangzhou,China,in3h.
Previously,thejourneytook11h.
Chapter 6AppliedMotion• MHR
NS Science 10 CH6.indd 253
253
12/3/11 3:10:04 PM
Check Your Understanding
7. Explain why the magnitudes for distance and displacement can be
different.
8. Describe how velocity and acceleration are related.
9. Why is it important to know how to do unit conversions?
Calculating Acceleration
The mathematical forms of the equations that describe acceleration are
very similar to those for velocity, as shown below. When you first look
at the units—metres per second squared—they might seem strange. A
brief analysis should clarify the meaning. When an object is accelerating,
the velocity is changing. The numerical value of the acceleration states
how much the velocity is changing. A value of 1.2 m/s2 means that the
velocity is changing by 1.2 m/s every second.
Did You Know?
Accelerationisthemeasure
oftherateatwhichvelocity
changes.InfreefallnearEarth's
surface,asonanamusement
parkridesuchastheonein
thephotograph,anobjectwill
accelerateat9.81m/s2.This
seemslikearatherlargerateof
accelerationuntilyouconsider
thefollowing:
•aratfleacanjumpwithan
accelerationof1350m/s2
•awoodpecker'sheadstops
withanegativeacceleration
of1200m/s2
•atroutcanstartswimming
withanaccelerationof
40m/s2
•amantisshrimpcanflailits
frontlegat104000m/s2
crushingitsprey
Acceleration
 v​
______
1
v​
2
​​or a  v​
aave  ___
ave
t

t1
t
2
where a​
ave is average acceleration
in metres per second squared,
m/s2
v​
​is the change in velocity in
metres per second, m/s
​
v​
​ 2 is the final velocity in metres
per second, m/s
​
v​
​ 1 is the initial velocity in
metres per second, m/s
t is the time interval in
seconds, s
​ t2 is the final time in seconds, s
​ t1 is the initial time in seconds, s
Unit Analysis
​
v​
​​
​ a​
​  ___
t
__
m
__
s
m  ___
__
s
s2
1
s
m  __
 __
s
1
1
m  __
 __
s
s
__
m
 2
s
Thisamusementparkrideinvolvesafreefallfromatowerthatis62mtall.
254
MHR•Unit 3Motion
NS Science 10 CH6.indd 254
12/3/11 3:10:06 PM
Direction of Acceleration
The direction of the acceleration is the same as the direction of the
change in the velocity. To determine the direction of the acceleration
from the initial and final velocities of an object, picture the direction
in which you would have to push on the object to cause the observed
change. The following examples will help you visualize the meaning of
the direction of the acceleration.
•
The initial velocity is in the positive direction.
The final velocity is in the positive direction and
the magnitude is larger.
The acceleration is in the same direction as the
initial velocity.
•
The initial velocity is in the positive direction.
The final velocity is in the positive direction, but
the magnitude is smaller.
The acceleration is in a direction opposite to the
initial velocity.
•
The initial velocity is in the positive direction.
The final velocity is in the negative direction. The
object slowed down, stopped, and began to move
in the opposite direction.
The acceleration is in a direction opposite to the
initial velocity.
•
The initial velocity is in the negative direction.
The final velocity is in the negative direction, but
�2
the magnitude is smaller.
The acceleration is in a direction opposite to the aaa���
initial velocity.
vv�1
1
vv�
11
vv�
�v��121121
vv�
vv�22
a�
�221
vvvaa�
aa�
��1221
vvaa�22
��2
vvv�
�vvaa�1111
vva�
��112112
vv�
vv�
22
va�
2
vva�
�vaa��122112
a�
�
vvvaa�
��222
vva�1
1
vvaa�
11
vv�
�v��121121
vv�
vv�22
2
vvaa�
��211221
vaa�
�a�
vvaa�22
v�
�2
vvaa�1
vvva�
�1111
vv�
��21121
vvv�
22
va�
2
vva�
�vaaa��121212
�
vvvaa�
�22
When solving problems mathematically, the sign—positive or
negative—of the answer will tell you the correct direction of the
acceleration. Practice this for yourself with the Sample Problem on the
next page. Then complete the Practice Problems. After solving each
problem, analyze the sign of the answer. Ensure that it gives the direction
that you would expect. This method is one way to check that your
answer is correct.
Did You Know?
Somedragonflies,liketheroyal
rivercruiser,Macromia taeniolata,
canaccelerateupto19m/s2while
chasingtheirprey.
Chapter 6AppliedMotion• MHR
NS Science 10 CH6.indd 255
255
12/3/11 3:10:08 PM
Sample Problem
Problem
A biologist observed a cheetah reach a velocity of 19 m/s from
a standing start in a period of 2.0 s. What was the cheetah’s
acceleration? Assume that the cheetah runs in a positive direction.
What Is Required?
You must calculate the acceleration of the cheetah.
What Is Given?
You know the initial velocity, v1  0.0 m/s.
You know the final velocity,​v2  19 m/s.
You know the time interval,t  2.0 s.
Plan Your Strategy
Use the formula that involves velocity and time to calculate
 v​
______
1
v​​​or a  v​
2
acceleration, a​
ave  ___
ave
t

t1
t
2
Act on Your Strategy
Place the known values into the formula and solve for the
unknown.
v​​​
aave  ___
t
m
m  0.0 __
19 __
s
s
 _______________
2.0 s
m
 9.5 __
s2
The cheetah’s acceleration is 9.5 m/s2 in the positive direction.
Practice Problems
17. In a record-setting race, a race car reached a velocity of
145.08 m/s in 4.48 s. What was the race car’s average
acceleration? Assume that the direction of the velocity is
positive.
18. A model rocket started from the ground and reached an
upward velocity of 66 m/s in 5.0 s. What was the rocket’s
average acceleration? (Let the upward direction be positive.)
19. A student on a bicycle decided to determine his acceleration
when coasting down a steep hill. The student started from a
full stop and reached a velocity of 8.75 m/s in 3.8 s. What
was his average acceleration? Assume that downhill is the
positive direction.
20. A car enters a highway travelling 14 m/s[N]. After 5.5 s,
the car reaches a velocity of 28 m/s[N]. What was the car’s
average acceleration?
256
MHR•Unit 3Motion
NS Science 10 CH6.indd 256
12/3/11 3:10:08 PM
Practice Problems—continued
21. A professional baseball pitcher pitches a ball, giving it a
velocity of 45 m/s toward the batter. The batted ball has
a velocity of 30 m/s toward the pitcher. Let the direction
from the batter to the pitcher be the positive direction. If the
change in velocity takes place over a period of 1.2 s, what was
the average acceleration of the baseball?
22. A child rolled a ball up a hill. At time zero, the ball had a
velocity of 1.8 m/s up the hill. After 6.5 s the ball’s velocity
was 2.3 m/s down the hill. Let uphill be the positive
direction. What was the average acceleration of the ball? What
is the meaning of the sign of the acceleration?
23. Objects near Earth’s surface fall with an acceleration of
9.81 m/s2. If you dropped a rock from a cliff over a river,
how fast would the rock be falling 4.1 s after you dropped it?
24. The average acceleration of the space shuttle at takeoff is
29 m/s2[up]. What is the shuttle’s velocity after 12 s?
Let up be the positive direction.
25. A car is initially travelling at a velocity of 4.2 m/s[W]. If the
car’s average acceleration is 0.86 m/s2[W], how long will it
take the car to reach a velocity of 9.6 m/s[W]?
Suggested Activity
Conduct an Investigation
6-2A, Investigating Canadian
Contributions to Motion
Did You Know?
A cheetah, Acinonyx jubatus, is
the world’s fastest land mammal.
A cheetah can go from 0 to
96 km/h in 3 s. That is a positive
acceleration of about 9 m/s2.
Did You Know?
Sailfish, Istiophorus platypterus,
are the fastest fish in the ocean.
They can reach speeds of up to
110 km/h.
Cheetah
Sailfish
Chapter 6 Applied Motion • MHR
NS Science 10 CH6.indd 257
257
12/4/11 3:17:58 PM
6-2A Investigating Canadian
Contributions to Motion
Conduct an InVesTIgATIOn
SkillCheck
• Planning
• ResearchingInformation
• OrganizingInformation
• Communicating
Materials
• computerswithInternet
access
• encyclopediasorother
researchmaterials
Canadianscientists,engineers,andinventorshavemademanycontributionsto
scienceandtosociety.Canadianshavecontributedtomanyareasofmotion,
includingimprovementstosea,air,andhighwaytravel.Canadianshavealsomade
contributionstoimprovedtravelduringadversetravelconditions,suchasindeep
snow.
Question
WhataresomeCanadiancontributionstomotion?
Procedure
1.Chooseatopicfromthelistbeloworresearchanothertopicofyourchoice.
Makesureyourteacherapprovesyourtopicbeforeyoubeginyourresearch.
Researchandanswerthefollowingfivebasicquestionsaboutyourtopic:who?
when?where?why?how?Besuretorecordthewebsiteaddress(URL)orbook
whereyougetyourinformation.
2.Produceareportinthemediumofyourchoiceandincludedetailssuchas
designcontributions,recentdevelopments,andglobalimpactofthedesign.
• AvroArrow
• SilverDart
• Gsuit
• variable-pitchpropeller
• snowmobile
• rotarysnowploughsfortrains
• CanadarmandCanadarm2
• nationalrailway
• bushplanes
• Canadairwaterbomber
• Trans-CanadaHighway
• ConfederationBridge
• St.LawrenceSeaway
• Bluenose
• BallardPowerSystems(fuelcells)
Analyze
1.Howdidyoudecidetousetheinformationresourcesthatyoudid?
2.Whyisitimportanttorecordthesourceofyourinformation?
Conclude and Apply
1.Howdidtheinventionthatyouinvestigatedaffectorchangemotion?
2.Istheinventionstillinusetoday?Explainyouranswer.
258
MHR•Unit 3Motion
NS Science 10 CH6.indd 258
12/3/11 3:10:17 PM
Checking Concepts
1. Describe a situation in which the distance
from one location to another location and the
displacement between the same two locations
are vastly different numbers. Use your school
as one of the locations.
2. Assuming that it took the same time interval
to go from location 1 to location 2 in
question 1, would the speed and velocity of
the trip be the same? Explain your answer.
3. Can the average speed of an object ever be
(a) equal to the magnitude of the average
velocity?
(b) less than the magnitude of the average
velocity?
(c) greater than the magnitude of the average
velocity?
Justify each answer.
4. Can the average velocity in an interval of time
be divided by the value of the time interval to
find acceleration? Explain why or why not.
5. Stefan concludes that the units for
acceleration of m/s divided by seconds can be
written as m/s/s or as m/s2. Are these valid
ways to report units for acceleration? Justify
your answer algebraically.
6. “The direction of the acceleration is always
the same as the direction of the change in
velocity.” Is this statement sometimes true,
always true, or never true? Justify your
answer.
7. An object with a velocity that is in the
positive direction experiences a short interval
of time during which the acceleration is
negative. Explain what will happen to the
velocity during this interval of time.
8. An object is moving north at 14 m/s when it
experiences 2.0 m/s2 acceleration in the same
direction it is moving. The object accelerates
for 4.0 s. What will be the velocity of the
object after the 4.0 s of acceleration?
Understanding Key Ideas
9. The displacement between Shelburne and
Yarmouth is 64.6 km[N50°W], while the road
distance is 80.8 km. If the entire trip took
1.5 h, what would be the average speed and
the average velocity of the trip?
10. Imagine that you can cross-country ski at a
pace of 3.7 m/s and it takes you 55 min to
reach the chalet from the last rest station on
the trail. What is the distance between the
chalet and the last rest station, in km?
11. It has been estimated that the average speed
of a sneeze is 150 km/h. How far would a
sneeze travel in 0.10 s?
12. A curling stone travelling at 2.0 m/s travels
for 12 s before coming to rest. What was the
average acceleration of the stone?
13. On the moon, the gravitational acceleration
rate is 1/6 that of Earth, or approximately
1.64 m/s2. If a moon rock were to be
dropped over the edge of a moon crater, how
fast would it be moving 3.50 s after it was
dropped?
14. A car is travelling at 38 m/s and brakes to
slow down. The negative acceleration is
1.25 m/s2 and lasts for 2.4 s. What will
be the resulting final velocity after the
acceleration?
Project Prep
Refertotheprojectattheendofthisunit.
Aretherewaystoincorporatewhatyouhave
learnedinthissectionintoyourproject?
Discussyourideaswithyourclassmates.
Chapter 6AppliedMotion• MHR
NS Science 10 CH6.indd 259
259
12/3/11 3:10:19 PM
Chapt er
6
In this chapter, you learned about accelerated
motion and how to calculate motion problems.
Create your own summary of the key ideas from
this chapter. You may include graphic organizers
or illustrations with your notes. (See Appendix
B for help with graphic organizers.) Use the
following headings to organize your notes.
1. Changes in Velocity
2. Using Motion Formula
Checking Concepts
1. What is responsible for the acceleration when
a car turns at an intersection?
2. Create a realistic displacement-time graph
of a dog running at 15 m/s for 10 s, then
coming to a full stop at its owner for 15 s.
3. Nando states that if the change in velocity
does not involve a change in direction,
acceleration can be reported as a scalar
quantity, but if the direction changes,
acceleration must be reported as a vector
quantity. Is this statement correct? Explain
your answer.
4. Determine the direction of the acceleration
in relation to the direction of the initial
velocity in the following situation:
The initial velocity is in the negative
direction. The final velocity is in the negative
direction and the magnitude is smaller.
5. Maria suggests that the scalar quantity
associated with acceleration would be a
change in speed over an interval of time, but
Raymond disagrees, stating that there is no
such scalar quantity. Who is correct? Justify
your answer.
6. An object had a velocity of 18 m/s[N] and
25 s later had a velocity of 18 m/s[S]. Clara
stated that since the speed was a constant
18 m/s, there was no acceleration. Is she
correct? Explain why or why not.
7. Can the gas pedal in a car ever cause negative
acceleration? Explain your answer.
8. An Olympic sprinter can reach her maximum
velocity of 10.2 m/s in the first 3.0 s of the
race. What is the acceleration during this
time interval? Assume the direction of the
velocity is positive.
9. Can acceleration cause an object to move
in the opposite direction to that in which
it is initially moving? If this is not possible,
explain why it is not. If it is possible, give an
example of when it could occur.
Understanding Key Ideas
10. An astronaut is repairing a sensor array
on the International Space Station when
she suddenly becomes detached from the
station and starts to slowly move away into
space. With no atmosphere in outer space to
provide resistance, she will continue to float
away unless she does something.
(a) Using concepts studied in this unit,
outline what she can do to get back to
the space station. Use terminology from
this unit to include an explanation of
how this process will get her back.
(b) Perform an Internet search to investigate
how astronauts in outer space deal with
this type of problem.
11. A car runs out of gas and coasts from
20 m/s[S] to rest 65 s later. Determine the
total displacement during this time interval.
12. Explain how the area under the velocitytime graph given here can be calculated from
t  0 s to t  25 s.
Velocity vs. Time
25
Velocity (m/s[E])
Prepare Your Own Summary
20
15
10
5
0
260
4
8
12
16 20 24
Time (s)
28
32
36
MHR•Unit 3Motion
NS Science 10 CH6.indd 260
12/3/11 3:10:22 PM
13. Use your method in question 12 to calculate
the displacement of the object in the given
graph.
14. The distance from Amherst to Pugwash
is 51.7 km and from Amherst to
Tatamagouche is 88.7 km. Tori passes a
point between Amherst and Pugwash at
noon and reaches Pugwash at 12:35 p.m. She
reaches Tatamagouche at 1:17 p.m. What
was her average speed between Pugwash and
Tatamagouche?
15. A truck travelled a distance of 475 m in a
time interval of 40.0 s. What was the speed
of the truck, in m/s?
16. A tennis ball moving at 35 m/s toward a
tennis racquet contacts the racquet for
0.85 s before it is sent back over the net at
38 m/s. What is the average acceleration of
the ball during this process?
17. Calculate the average acceleration in the first
8.0 s on the following graph.
Velocity vs. Time
Velocity (m/s[N])
100
80
60
40
20
0
2
4
6
Time (s)
8
10
18. A car is travelling at a velocity of
3.8 m/s[W] when it accelerates at
0.75 m/s2[W]. How long will it take for the
car to reach a velocity of 5.2 m/s[W]?
19. Sketch position-time graphs that illustrate
the following situations.
(a) zero velocity
(b) uniform motion
(c) increasing velocity
20. Describe the process for finding the velocity
of an object from a position-time graph of its
motion.
21. Sketch a velocity-time graph that illustrates a
positive acceleration.
22. A racehorse ran a 1.8 km race in exactly
2 min and 18 s. What was the horse’s
average speed?
23. A driver is on a highway that has provided
an odometer test zone in which signs mark
every kilometre for 25 km. He checks his
watch and sees that it is 1:16 p.m. when he
passes the 5.0 km marker. When he passes
the 25 km marker, his watch reads 1:31 p.m.
What was his average speed for that section
of the test zone?
24. Peregrine falcons are the fastest-diving
birds in the world. In fact, the peregrine
falcon is the fastest animal on the planet in
its hunting dive, called a stoop, in which it
soars to heights of 600 m and then dives
steeply towards its prey. During a stoop, the
peregrine falcon folds its wings and makes
its body shape as streamlined as possible,
reducing air resistance to almost zero. A
peregrine falcon dives with its talons closed
and strikes its prey in mid-air, knocking it
unconscious with a single blow. Then, as the
prey falls through the air, the falcon circles
back and plucks it out of the air. Starting
from rest at an altitude of 600 m, a peregrine
falcon was clocked diving at 320 km/h.
(a) What was its final velocity in m/s?
(b) Assuming air resistance is negligible,
how much time does it take the falcon to
reach this top speed?
(c) Sketch a velocity-time graph that shows
the dive. Let downward velocity be
negative.
Why It Matters
Inagroup,brainstormexamplesofhowthe
followingactivitiesmightrequireaworking
knowledgeoftheconceptsofmotion.
•aprofessionalcompetitiveskateboarder
•adirectorfilminganactionmovie
•amoderndancechoreographer
•atriathlonathlete
Chapter 6AppliedMotion• MHR
NS Science 10 CH6.indd 261
261
12/3/11 3:10:25 PM
Truck Driver
Constructionmaterials,suchas
lumber,bricks,andshingles,are
deliveredalloverCanadabytrucks.
The Canadian trucking industry currently employs approximately 235 000
drivers. The industry is constantly growing, and so is the need for well-trained,
qualified, professional truck drivers. Students who want to be truck drivers
should have clean driving records and no criminal record.
Drivers have to be able to calculate mathematical problems involving speed,
distance, and time, and they must take a test called the Test of Workplace
Essential Skills (TOWES) that evaluates numeracy and literacy skills. The
Commercial Safety College in Truro, NS, trains straight truck and tractortrailer operators. Their programs include safety training, manoeuvring skills,
and professional driver improvement. Alyson Sutherland, the college’s Truck
School Administrator, answers questions on how the principles of motion apply
to a trucker’s work.
What challenges do truck drivers face that involve distance,
speed, and time?
Weather,roadconstruction,andtraffic-relatedfactors,alongwithspeedanddistance,
havetobetakenintoaccountwhendriversaredetermininghowlongitwilltakethemto
getwheretheyneedtogo.Inaddition,onlongertripsdriversmuststaywithintheirlegal
drivingtimelimitssetbytheHoursofServiceRegulations.
When a truck driver sees an accident ahead of him or her on
the highway, is a basic understanding of how long it takes to
stop a large truck important and why?
Itisveryimportant.Driversmustbeabletoquicklydetermine,basedontheirspeedand
roadconditions,howlongitwilltakethemtostopthetruck.Theymustunderstandthe
relationshipbetweenstoppingdistanceandtheweightoftheirvehicle.Passengervehicles
canbestoppedalotfasterthanaloadedtractor-trailercanbe,andthemorecargothe
driversarehauling,thelongeritwilltakethemtostop.Thisisalsoafactorincalculatinga
safefollowingdistancebetweenthetruckandthetrafficaroundthem.
Mostitemsthatyoupurchasein
stores,suchasfood,shampoo,and
medicalsupplies,aredeliveredto
thestoresbytrucks.
How does an understanding of distance, speed, and time factor
into planning the route that a truck driver must take to deliver
the cargo?
Inadditiontolocalconditions,driverstakeintoaccountthedistancetheyneedtotravel
andlocalspeedlimitstodeterminehowmuchtimetheywillrequiretodelivertheirloads.
Beingabletoproperlycalculatethebestroutesavestimeandmoney.
How would taking a longer route than is necessary affect the
profitability of the trip?
Driversareusuallypaidbythekilometre,sotakinganunnecessarilylongroutewouldcost
thecompanymoremoneyindriverwages,fuelforthetruck,andpossiblelatefees.Itwill
takemoretime—timethatcouldbeuseddeliveringthenextscheduledload.
262
MHR•Unit 3Motion
NS Science 10 CH6.indd 262
12/3/11 3:10:29 PM
Motion at Work
The study of motion contributes to these careers, as well as many more!
Motion
Track &
Field Coach
Astronomer
Traffic Accident
Reconstructionist
Mechanical
Engineer
▲ Sprintingcoaches
monitorarunner’s
speedoverspecific
distances.Reducinga
runner’sspeedbyas
littleas0.01seconds
canmeanthedifference ▲ Everythinginthe
universe,includingEarth,
betweenanaverage
isinmotion.Astronomers
performanceanda
calculatehowfaraway
universityscholarship.
celestialbodiesare,where
theyaregoing,andhow
longitwilltaketoget
there.
▲
Engineerswhodesignmachinery
mustunderstandhowspeed,
distance,andtimerelateinthe
operationofeverythingfromthe
simplesttoolstoassemblyline
robotics.
▲ Basedonevidence,such
asskidmarksatthescene,
accidentreconstructionists
usetheirunderstanding
ofmotiontoinferhow
acollisionmighthave
occurred.
Over to You
1.Whatknowledgeaboutmotiondotruckdriversneed?
2.Researchanotherjobinvolvingmotion,andlist theskillsandknowledgethatyou
woulduseinthatjob.
Unit 3ScienceatWork• MHR
NS Science 10 CH6.indd 263
263
12/3/11 3:10:36 PM
Unit 3 Project
Game On!
Aneducationalpublisherhasaskedyourclasstocreateascavengerhuntgamethatteachestheconceptsinthis
physicsunittograde10studentsinNovaScotia.Toaccomplishthistask,youwillworkingroupstocreateseveral
prototypesofthisgame,whichyouwillthenplayandassess.
Problem
Howcanyouuseascavengerhuntgametoteachphysicsconceptstoothergrade10students?
Suggested Materials
•
•
•
•
•
•
•
measurementinstruments
paper,regularandgraph
pen,pencil,anderaser
ruler
calculator
stopwatch
digitalcamera(optional)
Procedure
1.Theeducationalpublishingcompanyhasprovidedguidelinesthatthegamemustfollow.
•Thegamemusthaveanintroductionthatincludesaclearandwell-organizedsummaryoftheconcepts
coveredinthisunit.
•Thegamemustprovidetencluesthatwillleadplayerstoanobjecthiddenonschoolproperty.(Teachers
purchasingthegamewillbeabletotweakthecluestoworkattheirschool.)
•Thecluesmustincludeeachofthefollowingmeasurementsatleastonce:distance,displacement,
speed,velocity,andacceleration.(Hint:Somemeasurementsmaybeusedincalculationstofindother
measurements.)
•Thecluesmustmakeuseofaleastonegraphandmayincludeonlythemathusedintheunit.
2.Usethemeasurementinstrumentsandothermaterialsprovidedtocreateyourgameprototype.
264
MHR•Unit 3Motion
NS Science 10 CH6.indd 264
12/3/11 3:10:47 PM
3.Check your prototype with your teacher. After your teacher reviews your prototype, you might be asked to revise
3.Checkyourprototypewithyourteacher.Afteryourteacherreviewsyourprototype,youmightbeaskedtorevise
it.Onceyouhavedoneso,yourteacherwillhideyouritematthelocationspecified.
4.Exchangeyourgamewithanothergroup.Playtheothergroup’sgametofindthehiddenitem.Usethe
stopwatchtorecordhowlongittakesyoutofindthehiddenitem.
5.Reporttoyourteacherafteryoufoundthehiddenitem.
6.Writeareviewthatdescribesthestrengthsandweaknessesoftheprototypeyouplayed.Provideyourreasoning
foreachassessment.
7.Exchangereviewswiththegroupyouexchangedprototypeswithinstep4.
Report
1.Readthereviewyoureceivedforyourprototype.Usethecommentsprovidedinthereviewandyourown
insighttoimproveyourprototype.
2.Createapresentationthatcommunicatesthemainfeaturesofyourprototype.Includethefollowing:
•yourintroductiontothegame,includingasummaryoftheconceptscoveredinthisunit
•yourcluesandanexplanationofhowyouimprovedthemafteryourprototypewastested
•anexplanationofhowyoucoveredthemotionmeasurementsinthisunitinyourclues
•ideasformarketingthiseducationalgame
3.Presentyourpresentationtoyourclass.
4.Evaluatealltheprototypesasaclassandchooseonetosendtotheeducationalpublisher.
Assessment Criteria
Onceyoucompleteyourproject,askyourselfthesequestions.Didyou...
•writeanintroductionthatclearlysummarizesthephysicsconceptscoveredinthisunit?
•create10cluesthatincludedistance,displacement,speed,velocity,andaccelerationmeasurementsatleastonce,
aswellasagraph?
•completeawell-reasonedassessmentofthestrengthsandweaknessesoftheprototypeyoutested?
•usetheassessmentyoureceivedandyourowninsighttoimproveyourprototype?
•createapresentationthatcommunicatesthemainfeaturesofyourprototype?
Unit 3Project• MHR
NS Science 10 CH6.indd 265
265
12/3/11 3:10:59 PM
UNIT
3
5
Investigating Motion
• When you describe the position of an object, you must include a distance, direction, and reference
point. (5.1)
• Units of length, such as metres and kilometres, are used to measure distance. (5.1)
• Compass points and coordinate systems are often used to describe positions. (5.1)
• Two ways of describing motion—a process of changing position—are distance and displacement. (5.1)
• A scalar is a quantity that has only magnitude, such as distance, time, and temperature. (5.1)
• A vector is a quantity that has both magnitude and direction, such as displacement and position. (5.1)
• Vectors are used to represent motion and they are added to find resultant vectors. (5.1)
• Position-time graphs indicate if an object is moving in the positive direction, in the negative
direction, or not moving at all. (5.1)
• Speed is the distance an object moves in a certain length of time. (5.2)
• Speed is a scalar quantity. (5.2)
• There are many kinds of speed, including constant speed, changing speed, average speed, and
instantaneous speed. (5.2)
• The slope of the line between any two points on a distance-time graph is the average speed the object
is moving during that time interval. (5.2)
• Velocity is a vector quantity that describes an object’s displacement during a specific time interval or
an object’s rate of change of position. (5.3)
• There are many kinds of velocity, including constant velocity, changing velocity, average velocity, and
instantaneous velocity. (5.3)
• The slope between any two points on a position-time graph gives the magnitude of the object’s
average velocity during that time interval. (5.3)
Applied Motion
6
• A change in the velocity of an object during a time interval is acceleration. (6.1)
• The change in velocity can be a change in the speed of the object, a change in the direction of the
object, or both a change in speed and direction of an object. (6.1)
• Analyzing a position-time graph gives you information about the velocity of the object. (6.1)
• Analyzing a velocity-time graph gives you information about the acceleration of the object. (6.1)
• During car rides, you experience zero acceleration, positive acceleration, and negative acceleration.
(6.1)
• Formulas are used to mathematically calculate speeds, velocities, distances, and displacements. (6.2)
266
MHR•Unit 3Motion
NS Science 10 CH6.indd 266
12/3/11 3:11:08 PM
Key Terms
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
average speed
average velocity
changing speed
changing velocity
constant speed
constant velocity
displacement
distance
instantaneous speed
instantaneous velocity
motion
position
reference point
scalar
speed
uniform motion
vector
velocity
Key Terms
• acceleration
Unit 3Summary• MHR
NS Science 10 CH6.indd 267
267
12/3/11 3:11:18 PM
UNIT
3
Visualizing Key Ideas
1. Copy and complete the following concept map using terms or phrases that are related to motion.
Ve
c
tor
ies
tit
qu
an
n
ua
rq
ala
tit
Sc
ies
Motion
s
pe
Ty
e
pe
fs
so
elo
dv
n
a
ds
ie
cit
Checking Concepts
2. What is used as the starting point to describe
the location of an object?
3. Explain the process of finding the
displacement between two points on a
number line.
4. Does the choice of a reference point affect
the displacement between two points?
Explain your answer.
5. List three examples of scalar quantities and
three examples of vector quantities.
6. Give an example involving constant speed
and an example involving changing speed.
7. At an average speed of 18.4 m/s, how long
will it take you to ride your bike 2.50 km?
Report your answer in seconds.
8. Explain when average speed and
instantaneous speed are equal.
9. If you were in a car that was moving at
25 km/h and your friend lived 8.3 km away,
how long would the trip take?
268
Slo
pe
so
na
po
sit
ion
-ti
me
gra
ph
10. Is the following statement true or false? If it
is true, explain why and if it is false, re-write
the statement to make it true.
You throw a ball upwards at 5.0 m/s. When
it gets back to your hand, it will have the
same velocity.
11. Give three situations that describe the
different ways that the velocity of an object
can change.
12. Give an example of each situation in
question 11.
13. Which type of graph is needed to calculate
the average velocity of an object using the
slope of the graph? Explain how this can be
done from the graph.
14. Regina described acceleration as the change
in speed over the interval of time that the
speed changed. Is she correct? Explain why
or why not.
15. Describe the feeling of acceleration on your
body. Include the cause of this feeling.
MHR•Unit 3Motion
NS Science 10 CH6.indd 268
12/3/11 3:11:20 PM
16. You are running around a circular track. You
run at a steady pace of 1.5 m/s. It takes you
2.5 min to run halfway around the track.
What is your average acceleration if you
started measuring time when you are facing
east and you stop measuring time on the
other side of the track when you are facing
west?
17. Describe how negative acceleration looks on
a position-time graph.
18. Describe the slope on a velocity-time graph
during a time interval in which acceleration
causes a steady decrease in the velocity of the
object?
19. Give a scenario in which each of the
following is true:
(a) average speed  magnitude of the
average velocity
(b) average speed  magnitude of the
average velocity
(c) average speed  magnitude of the
average velocity
20. Graph the data below on a velocity-time
graph. Then, write a story that explains the
motion in the graph.
Data Table
Time (s)
Velocity (m/s)[S]
0
0.0
5
10.0
10
15.0
15
7.5
20
12.0
25
15.0
23. Give one example of uniform motion and
one example of non-uniform motion.
24. Explain how the position-time graphs for
uniform motion and non-uniform motion
differ.
25. Find the displacement from position A to
position B in each of the following:
(a) d  12.4 m[E] and d  14.7 m[W]
A
B
(b) dA  18 km[S] and dB  22 km[S]
(c) dA  45.9 km[E] and dB  33.2 km[E]
26. A runner jogs around a circular track twice,
ending up where she started. If the radius
of the track is 75.0 m, determine the
factors below. (Hint: The formula for the
circumference of a circle is C  2r.)
(a) total distance travelled
(b) displacement
(c) Are these answers the same? Explain why
or why not.
27. On a position-time graph, north is chosen
to be positive. Describe the motion of the
objects with the graphed line segments
described below:
(a) a line segment with a negative slope
(b) a line segment with a zero slope
(c) a line segment with a positive slope
28. The right whale shown below is an
endangered species of whale that is found
off the coast of Nova Scotia. Right whales
are among the slowest swimming whales.
They can reach speeds up to 17 km/h. At
this speed, what distance will the right whale
travel in 0.5 h?
21. It takes you 15 min to get to school in the
morning. You average a speed of 14.1 m/s.
What is the distance from your house to the
school?
Understanding Key Ideas
22. You are 3 m north of a park, while your
friend is 5 m south of the same park. What is
the position and direction of the following?
(a) your friend with respect to your position
(b) you with respect to your friend’s position
29. When analyzing a piece of ticker tape from
a ticker tape timer, explain how you know if
an object was speeding up, slowing down, or
moving at a constant velocity.
Unit 3Review• MHR
NS Science 10 CH6.indd 269
269
12/3/11 3:11:22 PM
UNIT
3
30. Describe how average speed is calculated on
a distance-time graph.
31. Use the distance-time graph below to
calculate the average speed of the object
between the time interval t  1.0 s to
t  4.0 s.
Distance vs. Time
Position vs. Time
(1, 18)
16
40
12
(4, 9)
8
Position (m)[E]
Distance (m)
20
4
0
1
2
3
4
Time (s)
5
6
Data Table
Time (s)
30
20
10
32. Graph the data given below for two pet baby
rabbits, Olivia and Randy. Use the graph to
answer the questions that follow.
Olivia
Randy
Distance (m)
Distance (m)
0
0.0
0.0
10.0
5.0
3.5
20.0
10.0
7.0
30.0
15.0
10.5
40.0
20.0
14.0
50.0
25.0
17.5
(a) Does Olivia or Randy have the higher
average speed over the first 30.0 seconds?
Justify your answer.
(b) If the two can maintain the pace that
they have set, how far in front would the
faster rabbit be, if they were to continue
to move for 8.0 min? Show all work.
33. If you were in a car travelling, what two
instruments would you need to have to
be able to determine the instantaneous
velocity of the car you were in? Explain the
information obtained from each instrument.
270
34. Explain how the displacement of an object
can be determined if you are given a
velocity-time graph.
35. Determine the velocity of the object in each
time interval as represented in the following
position-time graph. The positive direction
for this graph is to the east.
0
4
8
12 16
Time (s)
20
24
36. What is the average velocity for the object in
the graph from question 35 in the following
time intervals:
(a) t  1 s to t  12 s
(b) t  5 s to t  15 s
(c) t  10 s to t  18 s
37. Use the graph in question 35 to answer the
following questions.
(a) Which interval was the object moving
the fastest?
(b) In which direction was the object
moving when it was moving the fastest?
(c) Determine the average speed and the
average velocity for the object over the
entire 21 seconds.
38. You maintain a constant velocity
of 2.85 m/s[W] for 3.0 min while
riding your dirt bike. What is your total
displacement over this interval of time?
39. A car is travelling at 22 m/s[E] for 15 s
when it starts to slow down uniformly until
it comes to rest 25 s after starting to slow
down. Determine the total displacement
during the total 40 s time interval.
MHR•Unit 3Motion
NS Science 10 CH6.indd 270
12/3/11 3:11:25 PM
40. A high performance sports car has a top
speed of 315 km/h and can accelerate from
0.0 to 100.0 km/h in 4.0 s. Determine the
acceleration of this vehicle, in m/s2.
41. You jog at a pace of 15.0 m/s for 10.0 s
before accelerating to 0 m/s over the next
10.0 s.
(a) Draw a velocity-time graph for this
motion.
(b) Determine the total displacement over
the 20.0 s time interval.
42. Create a position-time graph for an object
that experiences positive acceleration for a
time interval, followed by a time interval
with no acceleration and finally a time
interval with negative acceleration.
43. Create a matching strip of ticker tape to
match your graph in question 42.
44. You pass a highway sign as you travel with
your family that tells you the car is 395 km
east of your destination. Two hours later, a
new sign tells you that you are 247 km east
of your destination.
(a) What is the average velocity of your car
over this two hour time period?
(b) What assumption must be made in order
for the calculation in part (a) to be valid?
(c) If this assumption was not valid, what
would you have been able to calculate in
part (a)?
45. A race car like the one shown below, moves
77.2 m north from the starting point in
5.5 s. The car passes checkpoint 2 at 17.2 s
after leaving the starting point. The second
checkpoint is 153.5 m from the start line.
What is the average velocity of the car
between the two checkpoints?
46. An alligator, like the one shown below, can
run at a speed of 15.5 m/s, while it takes
an Olympic sprinter 10.0 s to run 102 m.
Image that the alligator and the sprinter were
in a 50.0 m long race.
(a) Which would win the race?
(b) By how many metres would the winner
be ahead at the finish line?
(c) What assumptions must be made for this
calculation?
47. A car covered a total distance of 825 m in a
total time interval of 55 s.
(a) Find the average speed of the car in this
time interval.
(b) Would the magnitude of the velocity be
larger or smaller than this average speed?
(c) Is it possible for the instantaneous speed
to have been larger than the average
speed at any point in the time interval?
Explain why or why not.
48. A truck is moving at a velocity of
3.8 m/s[N] when it accelerates with an
average acceleration of 0.50 m/s2[N]. How
long will it take for the truck to reach a
velocity of 6.7 m/s[N]?
49. An eastern diamondback rattlesnake,
Crotalus​adamanteus, like the one shown
below, can strike its prey in 0.2 s and spring
a distance of 0.5 m during the strike. What is
the speed of the rattlesnake during the strike?
Unit 3Review• MHR
NS Science 10 CH6.indd 271
271
12/3/11 3:11:30 PM