Name: ____________________________________________________
Period: ______
Unit I: Motion
Subunit B: Constant Acceleration
Chapter 2 Sections 2 and 3 Texas Physics p. 47-63
Equations
(figure 2.6 p.56)
Variables, Units
(ch 2 Summary p.72)
NOTES:
Method for problem solving
G:
U:
E:
S:
S:
Unit I-B Objectives
What you should know when all is said and done
1. Given a x vs. t graph, you should be able to:
a. describe the motion of the object (starting position, direction of motion, velocity)
b. draw the corresponding v vs. t graph
c. draw the corresponding a vs. t graph
d. determine the instantaneous velocity of the object at a given time
2. Given a v vs. t graph, you should be able to:
a. describe the motion of the object (direction of motion, acceleration)
b. draw the corresponding x vs. t graph
c. draw the corresponding a vs. t graph
d. write a mathematical model to describe the motion
e. determine the acceleration
f . determine the displacement for a given time interval
3. You should be able to determine the instantaneous velocity of an object in three ways:
a. determining the slope of the tangent to an x vs. t graph at a given point.
b. using the mathematical model vf = aΔt + vi
c. using the mathematical model vf2 = vi2 + 2aΔx
4. You should be able to determine the displacement of an object in three ways:
a. finding the area under a v vs. t curve
b. using the mathematical model Δx = ½ aΔt2 + viΔt
c. using the mathematical model vf2 = vi2 + 2aΔx
5. You should be able to determine the acceleration of an object in five ways:
a. finding the slope of a v vs. t graph
b. using the mathematical model a = Δv/Δt
c. rearranging the mathematical model Δx = ½ aΔt2 + viΔt
d. rearranging the mathematical model vf = aΔt + vi
e. rearranging the mathematical model vf2 = vi2 + 2aΔx
Unit 1B Reading/Notes
In the opening lab, the motion of an object rolling down an inclined ramp was
investigated. We did not concern ourselves with the rotational motion of the object and
instead imagined it as a point particle. By recording the position of the particle at equal
time intervals, a position vs. time graph was generated. The shape of the graph
appeared to be a top opening parabola.
In the constant velocity model, we established that the slope of the position-time graph
(change in position divided by change in time) is the average velocity during the time interval. The
slope of a straight line can be taken at any two points on the line because the slope is constant. So
what does the fact that the slope is not constant in our new experiment mean?
A changing slope on a position vs. time graph tells me that:
_______________________________________________________________________________
The average velocity can also be found for a curved position-time graph by the same method as for a
linear graph, by taking
totalbechange
in position
over
a time
interval. However,
onspeed
a curved
graph,
Whatthe
would
more useful
is to have
a way
of describing
the object’s
at a given
instant (or as
the slope is constantly
changing
at
each
point,
so
the
average
velocity
often
isn’t
a
very
good
Arons terms it: clock reading). To develop this idea, you must show that, as you shrink the time
description of the object’s
motion.
In order
find the
the object
at any(line
given
instant, orthe
the
interval Δt
over which
you to
calculate
thevelocity
averageofvelocity,
the secant
intersecting
curve at
instantaneous velocity,
a
line
can
be
drawn
through
two
points
to
first
find
the
average
velocity.
The
two points) more closely resembles the curve during that interval.
slope of What
this line
willbe
bemore
approximately
equal
to the
instantaneous
velocity
at at
some
point
exactly
would
useful is to have
a way
of describing
the object’s
speed
a given
instant
(or as
Arons
terms it:
clock
reading).
develop
thisisidea,
must
showthe
that,
as instantaneous
youxshrink the time
halfway in
between
these
points.To
(An
average
also
like
taking
two
velocities,
xtwo
x you
interval
!t over and
which
you calculate
thevaverage
adding them
together
dividing
by two:
+ vf)/2.) the secant (line intersecting the curve at
ave = (vi velocity,
two points) more closely resembles the curve during that interval.
Δx
x
x
Δt
t
Δx
xΔx
Δt
t
Δt
t
!x
!x As the interval gets
!x
That is, the slope of the secant gives the average
velocity for that interval.
shorter and shorter, the secant more closely approximates the curve.
!t Thus, the average velocity of
!t reasonable
t
this interval
a more and more
estimate of how fasttthe object is moving at any
t
!t becomes
instant during this interval.
That
is,two
the slope
ofare
the secant
the the
average
velocity
for that interval.
gets
The closer
the
points
on thegives
curve,
closer
the average
velocityAs
willthe
beinterval
to
x
shorter andAs
shorter,
the
more
closely
approximates
the
curve.
Thus,
the average
velocity of
the instantaneous
velocity.
Assecant
the
points
closer
closer,
they
a
one shrinks
thetwo
interval,
Δtget
to
zero,
theand
secant
becomes
areach
tangent;
this interval
becomes
a
more
and
more
reasonable
estimate
of
how
fast
the
object
is
moving
at any
point where
they meet
and
the
line
going
between
them
is
now
tangent
to
the
line
at
the slope of the tangent is the average velocity at this instant, or simply
instant
during
this
interval.
that point.
A tangent
line
touches
a
curve
at
just
one
point
without
crossing
from
one
the instantaneous velocity at that clock reading.
side of the curve to the other. The slope of the tangent tells us the velocity at the time
Δx
corresponding to the point on the graph to which the tangent is drawn. Since
x the
Asalways
one shrinks
the interval,
to find
zero,isthe
secant
becomes a tangent;
velocity is
changing,
what!twe
the
instantaneous
velocity.
Δt t
the slope
of
the
tangent
is
the
average
velocity
at
this instant, or simply
Student activity
theteacher
instantaneous
velocity
at thatyou
clock
reading.
Using
the x-ttaught
graphs
the students
produced
in the lab,
should
construct
least five tangents
Your math
may have
how
to find
the equation
forstudents
a parabola,
but
here in at
physics,
!
x
to
the
curve
and
determine
the
slope
of
each
tangent.
This
will
be
easier
if
the
students
have
we are going to use a concept called “linearization” to simplify the analysis of a graph by recognizing
a printed
out full-page graphs of their data or replotted their data on a sheet of graph paper. The students
pattern and creating a test plot that represents what model we expect the data to follow. You may
should then make a new graph of instantaneous velocity vs time. An alternative is to have students
know that a parabola is a graph that can also be called a “quadratic function”, or is represented
by an
t
!t tangents
enter
their equations into a graphing calculator and have the calculator draw
and determine
Student
activity
2
equation of y vs. xtheir
. If we
make
a
test-plot
of
position
vs.
time
squared
using
our
lab
data,
we
will
find
slopes
five clock
readings.
(See
or CASIO-slope.doc)
Using the x-t graphs
theatstudents
produced
in the
lab,TI-slope.doc
students should
construct at least five tangents
that the graph becomes linear; this means we can write the equation of the new test plot in the form
to the curve and determine the slope of each tangent. This will be easier if the students have printed
y = mx + b using position as the y variable and
time
squared as the
x. Therefore
weofcan
state
A plot
of instantaneous
velocity
(v,paper.
instead
v-bar)
vsthat
timethe
should yield
out full-pageUnit
graphs
of their data or replotted
their
data on a sheet
of graph
The
students
rsquared.
relationship between
theIII
variables was that position is directly proportional to time
Let’s try it!
v
Δ
should then make a new graph of instantaneous
vs time.
alternative
to≡have
students
a . That
is, the change in
a straightvelocity
line. The
slopeAn
of this
line is is r
t
Δ
enter their
equations
into
a
graphing
calculator
and
have
the
calculator
draw
tangents
and
determine
v
during
given time interval is defined to be the r
average
r r
their slopes at five clock readings. (Seevelocity
TI-slope.doc
or aCASIO-slope.doc)
v = at + v
Unit III
0 ,
acceleration. The equation for the line can be written as
r
v
where 0 isvelocity
the y-intercept.
It is important to define the acceleration this
(v, instead
Δv A plot of instantaneous
r of v-bar) vs time should yield
Unit III
v
Finding instantaneous velocity by determining the slopes of tangents will allow us to
create a plot of velocity vs. time. Making a graph of instantaneous velocity vs. time
yields a linear graph.
Δv
A linear graph (constant slope) of velocity vs. time tells me that:
Δt
t
_______________________________________________________________________________
The slope of the velocity vs. time graph is the change in velocity divided by change in time. It tells us
how much the velocity changes during each time interval. A large slope means that the velocity
changes a lot every second, whereas a small slope means that the velocity changes a 'Modeling
small amount
Workshop Project 2002
each second. Since the rate of change in velocity is a useful idea, we give it a name: acceleration.
Because both speeding up AND slowing down represent changes in velocity, they are both called
acceleration (no need for the odd term “deceleration”).
Acceleration:
_______________________________________________________________________________
Plotting the instantaneous velocity by determining the slopes of tangents will always work as long as
the acceleration is constant, but it is often a bit tedious (ok, a lot tedious!). So remember: When the
average velocity is determined for a time interval, we find that this average velocity is identical to the
instantaneous velocity at the time in the middle of the interval. For example, if the average velocity
from t = 2s to t = 4s is 10 m/s, the instantaneous velocity is 10 m/s at the time in the middle of the
interval, t = 3s. Let’s test this technique out on worksheet 1 to help us determine what the slope from
our new linearized graph represents!
Unit I-B: Constant Acceleration
Worksheet 1
t
(s)
0.0
x
(cm)
0.0
1.0
5.0
2.0
20.0
3.0
45.0
4.0
80.0
5.0
125.0
6.0
180.0
2
t
2
(s )
Δt
(s)
vave
(m/s)
Δx
(cm)
tmp
(s)
The data to the left are for a marble rolling
from rest down an incline. Use the positiontime data given in the data table to do the
following:
A) Plot a position vs. time graph for the data
on the axes below, using the entire graph
area. Label the graph clearly.
B) Complete the rest of the data table. For
the four columns on the right, you are
calculating the change from the previous
row to the subsequent row. tmp means the
mid-point time of the interval.
Position (cm)
0
1
2
3
4
5
6
7
8
Time (s)
C) Graph and label a test plot (to
linearize the data) on the grid, then
write the equation of the line below.
D) Plot and label a velocity vs.
time graph on the second grid. Be
sure to plot the time column that
makes your v vs. t graph an
instantaneous velocity vs. time
graph. Write the equation of the
line below.
g. Answer the 11 questions on
the following page!
1. What is the meaning of the slope of a position vs. time graph?
2. What is happening to the slope of your position vs. time graph as time goes on?
3. Explain what your answers to questions 1 and 2 tell you about the motion of the marble.
4. What is the meaning of the slope of your velocity vs. time graph? Explain!
5. Compare the slope of your velocity vs. time graph to the slope of your position vs. time2 graph.
What does this tell you about the slope of your position vs. time2 graph?
6. Write an equation that relates velocity and time for the ball using the mathematical analysis of your
velocity vs. time graph.
7. Write an equation that relates position and time for the ball using the mathematical analysis of your
position vs. time2 graph.
8. On the position vs. time graph, draw a line which connects the data point at t = 0 to the data point
at t = 6 s and calculate the slope of this line. Explain what the slope of this line tells you about the
motion of the ball.
9. On the position vs. time graph, draw a line which connects the data point at t = 2 s to the data point
at t = 4 s. Calculate the slope of this line. Explain what the slope of this line tells you about the motion
of the ball.
10. On the position vs. time graph, draw a line tangent to the graph at t = 3 s. Calculate the slope of
this line. Explain what the slope of this line tells you about the motion of the ball.
11. Compare the slopes you have calculated in questions 8, 9, and 10. Explain the results of your
comparison.
Unit I-B: Constant Acceleration
Worksheet 2
1. Accelerating objects are objects that are changing their velocity. Name the three controls on an
automobile that cause it to accelerate.
2. An object must be accelerating if it is moving _____. Circle all that apply.
A) with changing speed
D) in a circle
B) extremely fast
E) downward
C) with constant velocity
F) none of these
3. If an object is NOT accelerating, then one knows for sure that it is
A) at rest
C) slowing down
B) moving with a constant speed
D) maintaining a constant velocity
4. An object with an acceleration of 10 m/s2 will ____. Circle all that apply.
A) move 10 meters in 1 second
C) move 100 meters in 10 seconds
B) change its velocity by 10 m/s in 1 s
D) have a velocity of 100 m/s after 10 s
5. Ima Speedin puts the pedal to the metal in her Porsche and accelerates from 0 to 60 mi/hr in 4
seconds. Her acceleration is
A) 60 mi/hr
C) 15 mi/hr/s
B) 15 m/s/s
D) -15 mi/hr/s
Motion
in One Dimension
6. A car speeds up from rest to +16 m/s in 4 s. Calculate the acceleration.
Acceleration as a Vector Quantity
Acceleration, like velocity, is a vector quantity. To fully describe the acceleration of an object, one must
describe
theslows
direction
the acceleration
rule of the
thumb
is that if an object is moving in
7. A car
downoffrom
+32 m/s to vector.
+8 m/s A
in general
4 s. Calculate
acceleration.
a straight line and slowing down, then the direction of the acceleration is opposite the direction the object
is moving. If the object is speeding up, the acceleration direction is the same as the direction of motion.
following statements
andindicate
indicatethe
thedirection
direction(up,
(up,down,
down,east,
east,
west,
north
south)
of
9.8. Read
Read the following
statements and
west,
north
or or
south)
of the
the acceleration
accelerationvector.
vector.
10.
a.
Description of Motion
A car is moving eastward along Lake Avenue and increasing its speed
from 25 mph to 45 mph.
b.
A northbound car skids to a stop to avoid a reckless driver.
c.
An Olympic diver slows down after splashing into the water.
d.
A southward-bound free quick delivered by the opposing team is
slowed down and stopped by the goalie.
e.
A downward falling parachutists pulls the chord and rapidly slows
down.
f.
A rightward-moving Hot Wheels car slows to a stop.
g.
A falling bungee-jumper slows down as she nears the concrete
sidewalk below.
The diagram at the right portrays a Hot Wheels track
designed for a phun physics lab. The car starts at
point A, descends the hill (continually speeding up
from A to B); after a short straight section of track, the
car rounds the curve and finishes its run at point C.
Dir'n of
Acceleration
c.
b.
d.
c.
e.d.
2.
A curved line means
Which object(s) is(are) accelerating?
A gradually sloped line means
Which object(s) is(are) not moving?
A
steeply
slopedchange(s)
line means
Which
object(s)
its direction?
.
.
.
e. Which object is traveling fastest?
The motion of several objects is depicted on the position vs. time graph. Answer the following
10.questions.
The
motion moving
of several
objects
is depicted
onthan
the position
vs.ortime
graph.
the following
f. Which
object
ismay
traveling
slowest?
Each
question
have less
one, one,
more
thanAnswer
one answer.
questions. Each question may have less than one, one, or more than one answer.
g. A)
Which
is(are)
in rest?
the same direction as object B?
a. object(s)
Which
object(s)
is(are)
_____
Which
object(s)
is(are)moving
at rest?at
3.
4.
B) the
Which
object(s)
is(are)vs.
accelerating?
b.line
Which
object(s)
is(are)
The _____
slope of
on a velocity
time accelerating?
graph reveals information about an object's acceleration.
Furthermore,
the
area
under
the
line
is
equal
the object's displacement. Apply this understanding
_____ C) Which
object(s)
is(are) is(are)
not moving?
c. Which
object(s)
nottomoving?
to answer the following questions.
_____ D) Which
object(s)
change(s)
its direction?
d. Which
object(s)
change(s)
its direction? .
a. A horizontal line means
_____ E) Which
object object
is traveling
fastest?fastest?
e. Which
is traveling
b. A straight diagonal
line means
.
_____ F) Which
moving
object
is
traveling
slowest?
Which
moving
c. A graduallyf.sloped
line
meansobject is traveling slowest?
.
_____ G) Which object(s) is(are) moving in the same direction as
d. A steeply sloped
line means
. direction as object B?
g. Which
object(s) is(are) moving in the same
object B?
3. The slope of the line on a velocity vs. time graph reveals information about an object's acceleration.
The motion of several objects is depicted by a velocity vs. time graph. Answer the following
TheFurthermore,
motion of several
objects
is depicted
velocity
graph.
Answer the following
questions.
the area
under
the linebyisaequal
to vs.
thetime
object's
displacement.
Apply this
understanding
questions. Each question may have less than one, one, or more than one answer.
Each
question
may
have
less
than
one,
one,
or
more
than
one
to answer the following questions.
a. Which object(s) is(are) at rest?
answer.
a. A horizontal line means
.
_____ A) Which object(s) is(are) at rest?
b. Which object(s) is(are) accelerating?
b. A straight diagonal line means
.
_____ B) Which object(s) is(are) accelerating?
Which
object(s)
is(are)
notmeans
moving?
c.c. A
gradually
sloped
line
.
_____ C) Which object(s) is(are) not moving?
Which
object(s)
its direction?
d.d. A
steeply
slopedchange(s)
line means
.
_____ D) Which object(s) change(s) its direction?
e. Which accelerating object has the smallest acceleration?
_____ E) Which accelerating object has the smallest acceleration?
4. The
motionobject
of several
objects
is depicted
by a velocity vs. time graph. Answer the following
f. Which
has the
greatest
acceleration?
_____
F) WhichEach
object
has the may
greatest
acceleration?
questions.
question
have
less than one, one, or more than one answer.
g. G)
Which
object(s)
is(are)
moving
ininthe
_____
Which
object(s)
is(are)
movingat
thesame
samedirection
direction as
as object
object E?
E?
a. Which
object(s)
is(are)
rest?
b. Which object(s) is(are) accelerating?
c. Which object(s) is(are) not moving?
d. Which object(s) change(s) its direction?
© The Physics Classroom, 2009
e. Which accelerating object has the smallest acceleration?
Page 17
f. Which object has the greatest acceleration?
g. Which object(s) is(are) moving in the same direction as object E?
© The Physics Classroom, 2009
Page 17
Velocity Dir'n:
ty
Constant
+ Acceleration
nematic
Graphing:
sublevels
1-11 (emphasis on sublevels 9-11)
rection
Object moves in + Direction
+ or -
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Study Lessons 3 and 4 of the 1-D Kinematics chapter at The Physics Classroom:
or tion
Constant
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Direction
Speeding up or Slowing Down?
Velocity Dir'n:
Physics
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or
-
Graphing Summary
s/1DKin/1KinTOC.html
Constant + Acceleration
http://www.physicsclassroom.com/Class/1DKin/1KinTOC.html
Object moves in + Direction
MOP
Connection:
Graphing: sublevels 1-11
Unit
I-B:
Constant
Acceleration
Velocity
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or Slowing Down?
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Constant Velocity
(emphasis on sublevels 9-11)
Constant Velocity
he
1-D Kinematics
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Constant
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www.physicsclassroom.com/Class/1DKin/1KinTOC.html
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4 of the 1-D Kinematics chapter at The Physics Classroom:
Speeding
up or
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or
-
Graphing Summary
Velocity Dir'n:
+http://www.physicsclassroom.com/Class/1DKin/1KinTOC.html
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MOP Connection:
Kinematic Graphing: sublevels 1-11 (emphasis on sublevels 9-11)
Constant - Acceleration
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he 1-D Kinematics chapter at The Physics Classroom:Constant + Acceleration
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ation
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Object
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www.physicsclassroom.com/Class/1DKin/1KinTOC.html
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rection
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he 1-D Kinematics chapter at The Physics Classroom:
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Page 20 on sublevels 9-11)
nematic Graphing: sublevels 1-11 (emphasis
C)
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in the+- direction
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up
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tion
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Object moves in - Direction
Velocity Dir'n:
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+ Acceleration
© Constant
The Physics
Classroom, 2009
Object moves in + Direction
Velocity Dir'n:
Acceleration
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+
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-
Speeding up or Slowing Down?
Object moves in - Direction
Velocity Dir'n: + or Speeding
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Page 20
Constant - Acceleration
Object moves in - Direction
2009
-
Velocity Dir'n:
Down?
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Constant - Acceleration
Object moves in + Direction
Page 20
© Velocity
The Physics
Dir'n:Classroom,
+ or -2009
Speeding up or Slowing Down?
+ or -
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Constant - Acceleration
Object moves in - Direction
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Page 20
Velocity Dir'n: + or or Velocity
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2009
Page
20
© The Physics Classroom,
2009
Object moves
Velocity Dir'n
Speeding
upDir'n
or
Velocity
Speeding up or
Acceleration
-
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2. While cruising along a dark stretch of highway at 25 m/s (≈55 mph), you see, at the fringes of your
headlights, that a bridge has been washed out. You apply the brakes and come to a stop in 4.0s.
Assume the clock starts the instant you hit the brakes. Call the initial direction positive.
A) Construct a qualitative x vs. t graph of the situation described, and a quantitatively accurate
v vs. t graph to describe the situation.
Position (m)
Velocity (m/s)
Time (s)
Time (s)
B) On the v vs. t graph at right, graphically represent the car’s displacement during braking.
C) Utilizing the graphical representation, determine how far the car traveled during braking. (Show
work!)
2
Acceleration (m/s )
D) Determine the car’s acceleration, then sketch a
quantitatively accurate a vs. t graph.
E) Using the equation you developed for displacement of an
accelerating object determine how far the car traveled during
braking. (Show your work.)
0
Time (s)
F) Compare your answers to C and E.
14
v (m/s)
12
3. Use the following graph to answer questions for an object.
A) Give a written description of the motion.
9
6
3
0
-3
2
4
6
8 t (s)
2
4
6
8
-6
-9
B) Determine the displacement from t = 0s to t = 4 s.
-12
C) Determine the displacement from t = 4 s to t = 8 s.
D) Determine the average acceleration of the object’s motion.
v (m/s)
4. Use the following graph to answer questions for an object.
A) Give a written description of the motion.
8
6
4
2
B) Determine the displacement from t = 0s to t = 4 s.
0
-2
t (s)
-4
C) Determine the displacement from t = 4 s to t = 8 s.
-6
-8
D) Determine the displacement from t = 2 s to t = 6 s.
E) Determine the object’s acceleration at t =4s.
5. A car accelerates from rest to a speed of 20 m/s in a time of
5.0 seconds.
A) Sketch a velocity-time graph showing the motion of the car.
25
0
Velocity (m/s)
B) What is the acceleration of the car?
C) What distance will it travel as it accelerates? How do you
know?
14
Time (s)
Uniformly Accelerated Particle Model Worksheet 3:
Interpreting
Graphs of Accelerated Motion
Unit I-B: Constant
Acceleration
Object A:
Worksheet 4
1. The graph at right represents the motion of an
object.
A) Where on the graph above is the object
moving most slowly? How do you know?
B) Between which points is the object speeding
up? How do you know?
a. Where on the graph above is the object moving most slowly? How do you know? !
C) Between which points is the object slowing down? How do you know?
D) Where on the graph above is the object changing direction? How do you know?
b. Between which points is the object speeding up? How do you know?
2. A) For each line segment shown on the graph, identify if the acceleration and velocity are positive,
negative, or zero. Then decide if the object would be speeding up, slowing down, not moving, or
moving with constant velocity. Fill in the chart to show your answers. (also, see figure 2.3 on p.49)
Velocity (m/s)
v
a
Description
c. Between which points is the object slowing down? How do you know?
A
B
A
B
C
F
C
Time (s)
D
d. Where on the graph
direction? How do you know?
G above is the object changing
D
E
E
F
G
B) On the graph there is a dark black dot between sections C and D. What is the velocity at that exact
moment in time? What is the object doing? Is it still accelerating? Why or why not?
Motion in One Dimension
Name:
3. The motion of a two-stage rocket is portrayed by the following velocity-time graph. Several students
Interpreting Velocity-Time Graphs
analyze the graph and make the following statements. Indicate whether the statements are correct or
The motion
of a
two-stage
rocket
is portrayed
by thefeatures
following
velocity-time
incorrect.
Justify
your
answers
by referring
to specific
about
the graph.graph.
theisgraph
andinmake
the following
statements.
Indicate
whether
statements
A)Several
After 4 students
seconds,analyze
the rocket
moving
the negative
direction
(i.e., down).
Correct?
Yes the
or No
are
correct
or
incorrect.
Justify
your
answers
by
referring
to
specific
features
about
the
graph.
Justification:
Student Statement
Correct?
Yes or No
1. After 4 seconds, the rocket is moving in the negative direction (i.e.,
down).
B) The rocket is traveling with a greater speed during the time interval from 0 to 1 second than the
Justification:
time interval
from 1 to 4 seconds. Correct? Yes or No
Justification:
2. The rocket is traveling with a greater speed during the time interval from
0 to 1 second than the time interval from 1 to 4 seconds.
C) The firstJustification:
engine burns out quickly, but provides a higher acceleration. Correct? Yes or No
Justification:
3. The rocket changes its direction after the fourth second.
Justification:
D) During the time interval from 4 to 9 seconds, the rocket is moving in the positive direction (up) and
slowing down. Correct? Yes or No
Justification:
4. During the time interval from 4 to 9 seconds, the rocket is moving in the
positive direction (up) and slowing down.
Justification:
E) At nine seconds, the rocket has returned to its initial starting position. Correct? Yes or No
Justification:
5. At nine seconds, the rocket has returned to its initial starting position.
Justification:
F) During the time interval from 9 to 14 seconds, the rocket is slowing down in the negative direction.
Correct? Yes or No
Justification:
© The Physics Classroom, 2009
Page 19
4. The following graph shows Shopping Sandy’s velocity as she races up and down the walkway in
North Star Mall trying to find the perfect pair of capris. Answer the questions below.
Velocity (m/s)
6
4
2
Time (s)
0
-2
-4
-6
0
4
8
12
16
20
24
28
32
36
40
A) Describe Sandy’s motion.
B) During what time periods is Sandy accelerating? Find Sandy’s acceleration for each time period.
C) What is Sandy’s displacement from t = 6s to t = 14s?
D) What is Sandy’s displacement from t = 14 s to t = 22 s?
E) What is Sandy’s displacement from t = 30s to t = 36s?
Unit I-B: Constant Acceleration
Worksheet 5
1. A bicycle starts from rest and reaches a speed of 2.5 m/s during
a time of 5 seconds.
A) Draw a velocity-time graph for the bicycle.
5
Velocity (m/s)
B) What was the bicycle’s acceleration?
C) How far did the bicycle travel during this time?
14
2. A resting cat gets startled by a dog. It turns and runs with an
acceleration of 8 m/s2, reaching full speed in only 0.8 seconds.
A) What is its final velocity?
5
Time (s)
Velocity (m/s)
B) What distance does the cat cover as it accelerates?
14
Time (s)
C) Make a velocity-time graph for the cat.
3. An old clunker car can accelerate from rest to a speed of
28 m/s in 20 s.
A) Draw a velocity-time graph for the car.
5
Velocity (m/s)
B) What is the average acceleration of the car?
C) What distance does it travel in this time?
14
Time (s)
4. A motorcycle goes from 15 m/s to a dead stop in 3 seconds.
A) Draw a velocity-time graph for the motorcycle.
5
Velocity (m/s)
B) What is its acceleration?
C) What distance will it travel?
14
5. An ostrich has an acceleration of -2 m/s2. If it is initially traveling
at a velocity of +7.5 m/s,
A) How long will it take to completely stop?
5
Time (s)
Velocity (m/s)
B) What distance will it travel?
14
Time (s)
C) Draw a velocity-time graph for the ostrich.
6. A Hot Wheels car accelerates down a 5-meter long ramp. If the car takes 2.5 seconds to reach the
bottom of the ramp,
Velocity (m/s)
A) What is its acceleration?
5
B) What is the speed of the car at the bottom of the ramp?
C) Draw a velocity-time graph for the car.
14
Time (s)
5
7. An airplane accelerates down a runway at 3.0 m/s2 for 33 s until
is finally lifts off the ground.
A) Determine the distance traveled before takeoff.
Velocity (m/s)
B) What is the airplane’s lift-off velocity?
14
Time (s)
C) Draw a velocity-time graph for the airplane.
8. A bullet leaves a rifle with a muzzle velocity of 521 m/s.
While accelerating through the barrel of the rifle, the bullet
moves a distance of 0.840 m.
A) Determine the acceleration of the bullet.
5
Velocity (m/s)
B) How long was the bullet traveling inside the barrel of the gun?
14
C) Draw a velocity-time graph for the bullet.
Time (s)
Unit I-B: Constant Acceleration
Worksheet 6
1. A bear spies some honey and takes off from rest, accelerating at a rate of 2.0 m/s2. If the honey is
16 m away, how fast will he be going when he reaches it?
2. At t = 0 s, a car has a speed of 30 m/s. At t = 6 s, its speed is 14 m/s. What is its average
acceleration during this time interval?
3. A bus initially moving at 20 m/s slows at a rate of 4 m/s each second.
A) How long does it take the bus to stop?
B) How far does it travel while braking?
4. A physics student skis down a hill, accelerating at a constant 2.0 m/s2. If it takes her 15 s to reach
the bottom, what is the length of the slope?
5. As a car passes, a dog runs down his driveway to chase it with an initial speed of 5 m/s, and
uniformly increases his speed to 10 m/s in 2 s.
A) What was his acceleration?
B) How long is the driveway (TOTAL displacement)?
6. A mountain goat starts a rockslide and the rocks crash down the slope 100 m. If the rocks reach the
bottom in 5 s, what is their acceleration?
7. A car whose initial speed is 30 m/s slows uniformly to 10 m/s in 5 seconds.
A) Determine the acceleration of the car.
B) Determine the displacement of the car.
UnitEI-B:
Constant
Acceleration
Wile
Coyote
on the Planet
Newtonia
WileWorksheet
E slipped off the edge
of a tallE.
building
and wason
photographed
7: Wile
Coyote
the
at one second intervals as he underwent free fall. Complete the
Planet Newtonia
table below, plot final velocity vs time, then answer the questions.
(Start of Section 2.3 p.58)
(s)
yoff
(m)the edge
Wile ETslipped
of a tallVfbuilding
(m/s) and was
V (m/s)
photographed at one-second intervals as he underwent free
fall. Complete the table below, plot final velocity vs. time,
then answer the questions.
T
y
Vave
Vf
(s)
(m)
(m/s)
(m/s)
0
1
2
3
4
5
1. Write the equation for the graph above.
2. Using your graph, determine the value of the
1. Write the
equation for the graph above.
acceleration.
2. Using your graph, determine the value of the acceleration.
3. Using your graph, determine the displacement
during the first 3 s.
3. Using your graph, determine the displacement during the
first 3 s.
4. Using
the mathematical
model,
determine
the
4. Using
the mathematical
model,
determine
the
displ
cement
during
the
first
3
s
displacement during the first 3 s.
Wile E. Coyote in Free Fall on Newtonia’s Moon
Wile E. slips off the edge of a cliff and was phototgraphed at one second intervals as
he underwent free fall. Complete the table below, plot final velocity vs time, then
answer the questions.
Wile E. Coyote in Free Fall on Newtonia’s Moon
Wile E. slips off the edge of a cliff and was
photographed at one-second intervals as he
underwent free fall. Complete the table below, plot
final velocity vs. time, then answer the questions.
T
y
Vave
Vf
(s)
(m)
(m/s)
(m/s)
0
1
2
3V
4
5
6
t
1. Write the equation for the graph above.
2. Using your graph, determine the value of the
acceleration.
3. Using your graph, determine the displacement during
firstthe
3 s.equation for the graph above.
1.the
Write
Using
graph, determine
the value
4.2.Using
theyour
mathematical
model, determine
the of the
acceleration.
displacement during the first 3 s.
3. Using your graph, determine the displacement
5. How does the gravity on the moon compare to that
during the first 3 s.
of Newtonia?
4. Using the mathematical model, determine the
displacement during the first 3 s.
5. How does the gravity on Newtonia’s moon compare to that of Newtonia?
Unit I-B: Constant Acceleration
Worksheet 8: Free Fall
1. A ball is dropped from the top of the Leaning Tower of Pisa, 70 m above the ground.
A) How long does it take to hit the ground?
B) What will be its velocity the moment it hits the ground?
2. Now the ball is thrown down from the tower with an initial velocity of 3 m/s.
A) Now how long does it take to hit the ground?
B) What will be its final velocity now?
3. A ball is thrown straight up into the air with an initial velocity of 15 m/s.
A) How high does it go?
B) What is the ball’s hang-time (how long is it in the air)?
4. A kangaroo jumps to a vertical height of 2.5 m. What was its hang-time?
5. You drop a rock in a well and see it hit the bottom in 2 seconds. How deep is the well?
6. A feather is dropped on the moon from a height of 1.40 meters. The acceleration of gravity on the
moon is 1.67 m/s2. Determine the time for the feather to fall to the surface of the moon.
7. Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the
ground. Determine the time required for the shingles to reach the ground.
8. Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s.
Determine the height to which the vase will rise above its initial height.
9. Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.6 seconds, what will
be his final velocity and how far will he fall?
Unit I-B: Constant Acceleration
Worksheet 9: Stacks of kinematics curves
Given the following position vs. time graphs, sketch the corresponding velocity vs. time and
acceleration vs. time graphs.
For the following velocity vs. time graphs, draw the corresponding position vs. time and
acceleration vs. time graphs.
Unit I-B: Constant Acceleration
Review Worksheet
1. A) Give a written description to describe the motion of
this object.
B) Determine the instantaneous velocity of the object at
t = 2 s and explain how you did it.
C) Assume the initial velocity was 8 m/s; determine the
acceleration of the object.
D) Sketch a corresponding velocity-time graph.
2. Use the graph to answer the following questions.
A) Describe the motion of the object.
B) Determine the acceleration of the object from the graph.
C) Calculate the object's displacement from 0 to 6 seconds using either the graph or an equation.
3. A car, initially at rest, accelerates at a constant rate of 4.0 m/s2 for 6 s. How fast will the car be
traveling at t = 6 s? (Show your work!)
4. A tailback initially running at a velocity of 5.0 m/s becomes very tired and slows down at a
uniform rate of 0.25 m/s2. How fast will he be running after going an additional 10 meters?
5. A cliff diver jumps from a cliff and lands in the ocean water after 3.5 seconds.
A) What is the height of the cliff?
B) What was the velocity of the diver upon entering the water?
6. A ball player catches a ball 4 seconds after throwing it vertically upward.
A) With what speed did he throw it?
B) How high did it go?
7. Using the graph, compare the following quantities for objects A and B. Is A > B, A < B, or A = B?
A) Displacement from 0 to 3 s ___________ How do you know?
This image cannot currently be displayed.
B) Average velocity from 0 to 3 s ___________ How do you know?
C) Instantaneous velocity at 3 s ___________ How do you know?
8. For each of the position vs. time graphs shown, draw the corresponding v vs. t and a vs. t graph