Unit 1: Motion - SAMPLE

INQUIRY PHYSICS
A Modified Learning Cycle Curriculum
by Granger Meador
SAMPLE of Unit 1: Motion
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Version 2.0D В©2014 by Granger Meador
INQUIRY PHYSICS
inquiryphysics.org
A Modified Learning Cycle Curriculum
by Granger Meador, В©2010
Unit 1: Motion
Teacher’s Guide
these TEACHER’S GUIDES are copyrighted and all rights are reserved
so you may NOT distribute them or modified versions of them to others
However, the STUDENT PAPERS, SAMPLE NOTES, and any PRESENTATIONS for each unit
have a creative commons attribution non-commercial share-alike license; you may
freely duplicate, modify, and distribute them for non-commercial purposes if you give
attribution to Granger Meador and reference http://inquiryphysics.org
1 Motion
Teacher's Guide
Inquiry Physics
Key Concepts
Speed is the m easurable rate of change in the position of an object. Acceleration is the m easureable rate
of change in speed. Both graphical and num erical representations of position, speed, and acceleration
can be utilized to describe and predict m ovem ent.
Student Papers
Lab: Galilean Ram p (analyze m otion of ball/cart down a track)
W orksheet A: Calculating Motion (initial m otion problem s and a graph)
W orksheet B: Interpreting Motion Graphs
W orksheet C: Com bining the Variables of Motion (form ulating additional equations)
W orksheet D: 1-Dim ensional Motion Problem s
W orksheet E: Quiz Review
Introduction
Students are aware that such ideas as speed, velocity, and acceleration exist, but they are often unaware
of how to distinguish one of those ideas from another. Since the students are not proficient with the
concept of vectors, this investigation only uses speed. Do NOT feel com pelled to introduce the velocity
concept here; that will com e later in unit two. Tell the students that the sym bol v will be used for speed to
avoid confusion later on.
Three key equations arise from this investigation:
Average speed is the change of distance with respect to tim e, or
Acceleration is the change of speed with respect to tim e, or
If acceleration is constant, average speed is also given by
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
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UNIT 1: MOTION Lab: Galilean Ramp, pages 1-3
Pre-Lab
Preface this lab with definitions, exam ples, and discussion of accuracy, precision (or tolerance, depending
on your text or personal usage), and parallax. Also instruct them on the proper use of significant figures,
and refresh them on the basic m etric system (SI) prefixes. Also refresh your students on the basic
equations and graphical form s of linear, parabolic, and hyperbolic functions. This will help them interpret
their graphed data and develop the concepts regarding d vs. t, v vs. t, and a vs. t graphs.
Exploration
Equipm ent for each group (of 3 to 4 students):
grooved wooden track OR air track OR other dynam ics track with ball or cart, about 1.5 to 2 m long
if using a wooden track, a 7 m m groove should run lengthwise along the track for a steel ball
(e.g. large ball bearing) to roll along; a wooden block or other stop will be needed at the bottom of
the track
ring stand OR blocks to incline the track
ball for wooden track (diam eter $ 2 cm and m ass $ 60 g) OR air track glider OR wheeled toy/cart
m eter stick - show the students how to read the m eter stick to as m any decim al places
(precision/tolerance) as possible; typically they'll be reading 3 to 4 significant figures
stopwatch
m asking tape (unless track is ruled)
PART ONE:
Only pass out the first two pages of the lab to begin with; the third page is designed to be pre-loaded into a
printer for printing of a distance vs. tim e graph (or students can put a hand-plotted graph in that space).
The fourth page is sim ilarly designed for a speed vs. tim e graph, and will not be used until a day or two
after the lab begins. Don’t worry if your students can’t use com puters or calculators - later in this guide
you’ll be shown how to handle a parabolic relationship without such equipm ent.
For the data collection, each group should set up the equipm ent in exactly the sam e way so that the class
data can be com piled, com pared, and used to invent the concepts. Each student in a group should have
an assigned role (e.g. ball/cart release, tim ing, recorder, and ball/cart stop and return). For this first lab,
stress that students should check each other on their m easurem ents.
Before the students collect data, discuss with them the various experim ental errors to be avoided or
m inim ized, such as: which part of the ball or cart is to be held at the m ark on the tape (the front, not the
m iddle or back), how should the release and tim ing be coordinated (verbal cue from tim er), how the
ball/cart should be released (by swiping a pencil held in front of it straight down the track away from the
ball/cart, not pulling it upward or sideways to avoid backroll and spin), and why the longest run is
m easured first (because it is the one least affected by tim ing errors; the shorter runs where tim ing errors
are m ore significant are saved for the end when the experim enters are m ore practiced).
PART TW O:
The labs are written so students could, if desired, use the Graphical Analysis program from Vernier
Software (www.vernier.com ) to input and graph their data. Space has been left blank on lab pages 3 and
4 so that they can be pre-loaded into a printer. Another option is for students to analyze the m otion using
Microsoft Excel or another spreadsheet, or to graph the data by hand. I do NOT advocate using
probeware to analyze the m otion, as this can easily short-circuit the developm ent of the concepts. Delay
using probeware until after unit two, when the vector concepts are in place; one can then have students
predict and analyze m otion graphs collected as they m ove in front of a m otion detector.
If using a calculator or com puter to graph, first show the students how to use the m achinery. Have them
m ake their graphs, get them approved, print them , and answer the questions on lab pages 2 and 3. In the
approval process, check that they have plotted (0,0); if they haven't, engage them in a discussion to
illustrate its validity.
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UNIT 1: MOTION Lab: Galilean Ramp, pages 1-3
W hat if my students do not have access to a computer or calculator for graphing?
Many of the graphs in this curriculum are linear, so students can sim ply plot the points by hand and
eyeball a best-fit line. Careful plotting and drawing of the best-fit line will yield equations with useful slope
values. However, in this first lab they face a squared relationship, and hand-drawn parabolas are seldom
accurate.
If your students need to construct graphs by hand (or if the graphing software cannot handle quadratic
fits), that need not prevent them from decisively determ ining the num erical relationship between distance
and tim e. They’ll just need to draw two different graphs - one to determ ine the type of relationship and the
second to find the num erical values in it. You will probably need to lead them through the process with
sam ple data or a class average.
1.
Plot the data and note the shape of the best-fit curve and its general meaning.
First have the students graph distance vs. tim e (tim e always goes on the x-axis, even when it is
the dependent variable). Have them eyeball a best-fit curve to the data points, which should yield
a reasonable half-parabola. You will then need to ask them to identify the m athem atical m eaning
of that shape, or lead them to realize that it im plies that distance is directly proportional to the
square of tim e.
2.
Re-compute for the discovered relationship and re-plot accordingly.
The next step is to test for that squared relationship. The students will now com pute the square of
the tim e for each part of the experim ent. Then have them graph distance on the y-axis and time
squared on the x-axis. If their data is good, the points should plot out in a roughly straight
diagonal line.
3.
A squared relationship will yield a straight line on the second graph.
Ask the students what the line m eans. It m eans that distance is directly proportional to the square
of tim e. Have them eyeball a best-fit line for the second graph. (Here it is useful to rem ind them
that a best-fit line need not hit even a single plotted data point nor go through the origin. A best-fit
line runs through the “m iddle” of the data point distribution.)
4.
Using the slope of the best-fit line to obtain the relationship.
Once the students have drawn the best-fit straight line, have them com pute its slope. The
resulting equation will be d = k t2 + b where d is the distance, k is the slope, t2 is the square of the
tim e, and b is the graph’s y-intercept. Voila! They now have about the sam e equation a fancy
com puter or calculator would have calculated when form ing a best-fit parabola to the original
distance vs. tim e graph (the only difference is that the t term in the quadratic autom atically has a
coefficient of zero: d = k t2 + 0 t + b).
5.
Use the results.
Now the students can fill in the equation for the graph and m ove on. If you have them m ake any
predictions about distance or tim e, have them use the second graph (the linear one of d vs. t2)
since the best-fit line will likely be m ore true to the data than the best-fit parabola.
Do NOT assum e students will easily follow all of this! A com m on error is thinking that the second graph
indicates distance and tim e (instead of tim e squared) are directly proportional. Som e students will sim ply
go through the drill of m aking the graphs without thinking about what they are doing, unless you question
them verbally or in written form .
Sam ple answers for those two pages are shown next.
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
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UNIT 1: MOTION Lab: Galilean Ramp, pages 1-3
Distance (cm)
Time (s)
Average Time (s)
5.20
175.00
HAVE THE
STUDENTS
LEAVE THIS
COLUMN BLANK
UNTIL LATER,
WHEN THEY
WILL
CALCULATE THE
SPEED AND
RECORD IT
HERE
4.38
150.00
4.08
125.00
3.53
100.00
2.74
75.00
2.55
50.00
1.93
25.00
The Idea answer all questions in complete sentences
1.
Identify the independent and dependent variables in this experiment.
The answer
is not available
in this online variable,
sample. and the time is the dependent
The distance
is the independent
variable.
Create a graph of distance traveled along the incline versus average time. Graphs involving time always plot time horizontally on the
x-axis and the other variable vertically on the y-axis. This can violate the usual practice of placing the independent variable on the x-axis
and the dependent on the y-axis.
You need to decide if (0,0) is a valid point to include. Make sure each member of the group has a graph.
2.
What is the shape of the line on your graph? (Is it straight or is it curved? If it is curved, state whether it looks parabolic or
hyperbolic, etc.)
The answer
is not available
in this online sample.
It is curved,
like a parabola.
3.
The shape of a graph illustrates the mathematical relationship between the independent and dependent variables. What does
your graph specifically show you about the relationship between distance and time?
The answer
is not available
in this
online sample.
The distance
is directly
proportional
to the square of the time.
4.
Express the relationship you described in question 3 as a proportionality: Not
d%
5.
According to the graph, what was the ball/cart doing as it went down the track?
2
in sample.
tavailable
The answer
is not available
in this online sample.faster.
It was speeding
up/accelerating/moving
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
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UNIT 1: MOTION Lab: Galilean Ramp, pages 1-3
6.
The graph has a best-fit curve. What type of fit did you perform, or instruct the computer or calculator to perform (linear,
quadratic, inverse, etc.)?
The answer
is not
available fit.
in this online sample.
We used
a quadratic
7.
In question 4, you expressed the basic proportionality between the independent and dependent variables. Your best-fit curve
allows you to now express the precise equation for your group's data. Use your graph to fill in the missing values in this
equation. Round off the values to the appropriate number of significant figures.
-3.74
12.4
4.54
d = ________ + ________ t + ________ t2
Soon we will examine how the speed of the ball/cart was changing.
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
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UNIT 1: MOTION Lab: Galilean Ramp
Using pages 1-3 to develop concepts:
Conceptual Invention
Com bine the student graphs either using transparencies or, m ore effectively, by inserting each group's
data into a single Graphical Analysis or other program file and having the com puter perform a best-fit
curve for the entire data set. Discuss the graphs and the answers to questions 1 through 7.
You will need to em phasize on question 3 how the graph shows that distance is proportional to the square
of tim e, and NOT tim e is proportional to the square of distance.
Students often read too m uch or too little into answering question 5. Help them realize that the graph
indicates distance is rising at a faster rate than tim e: that the ball/cart is covering m ore and m ore distance
during each tim e interval as it rolls down the track. The use of the term acceleration should be neither
discouraged nor encouraged; do not attem pt to define acceleration yet.
Ask the students what units distance over tim e would have. (They should respond m /s.) Now you can tell
them that distance divided by tim e is called speed and is sym bolized by a v to form their first
equation:
Note that the bar over the v has been om itted for now, because the concept of average speed has not
been developed.
Do not accept the term velocity for now; tell them they will deal with that idea later. Em phasize how speed
is always expressed in units of distance over tim e (e.g. m /s, m i/h, furlongs/fortnight).
Expansion of the Idea
Instruct the students on the proper approach to problem -solving and showing all of their work.
For exam ple:
1.
State givens
2.
Show original equations being used
3.
Show all work, including units (show num bers plugged into the equation, and always show the
units on any m easurem ent)
4.
Round the answer to the proper significant figures and box it
W ork an exam ple out with them in their notes, and then assign W orksheet A, their first problem set.
Sam ple answers for W orksheet A are shown next.
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
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UNIT 1: MOTION Worksheet A: Calculating Motion
Worksheet A: Calculating Motion
1. The Spirit and Opportunity robot rovers landed on Mars in 2004 and explored it surface for years.
The rovers’ spacecraft and the rovers themselves travelled at wildly different speeds.
a.
The Spirit rover could move across the Martian landscape at a maximum of 2.68 m/min.
How many minutes would it take for it to travel 10.4 m, the length of a typical classroom?
v = 2.68 m/min
d = 10.4 m
t=?
b.
t=d/v
= (10.4 m)/(2.68 m/min) =
= 3.8806 min
3.88 min
Spirit journeyed to Mars in a spacecraft that traveled about 487 gigameters (487Г—109 m or
303 million miles) from Earth to Mars, averaging about 27,100 m/s (60,600 mi/h). Use the
SI units to calculate how many Earth days it took for the spacecraft to complete its journey.
d = 487Г— 10 9 m ( or 4.87 Г— 1011 m)
v = 27,100 m/s
t = ? days
t = d / v = (487 Г— 10 9 m) / (27,100 m/s) = 17,970,480 s = 17,970,000 s
208 days
=
2. A runner in a 1.00Г—102 meter race passes the 40.0 meter mark with a speed of 5.00 m/s.
a.
If she maintains that speed, how far from the starting line will she be 3.00 seconds later?
tThe
= 3.00
s is not availabledinrunthis
= vonline
t = (5sample.
m/s)(3 s) = 15 m
answer
v = 5.00 m/s
dstart = ?
dstart = 40 m + drun = 40 m + 15 m =
b.
55.0 m
If 5.00 m/s was her top speed, what is the shortest possible time for her entire 1.00Г—102 m run?
dThe
= 100
m is not available in this online sample.
answer
v = 5.00 m/s
t = d / v = (100 m) / (5 m/s) =
t=?
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
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20.0 s
P AG E 8 O F 18
UNIT 1: MOTION Worksheet A: Calculating Motion
3.
The graph above describes the motion of a golf ball. Note that it graphs distance from a position, not distance traveled. The
ball is placed on the green at 5 meters from the cup at t=0 seconds.
a.
How far from the cup was the ball at t=1 second?
5 meters
Answer
not available in online sample.
b.
What was the speed of the ball at t=1 second?
c.
How far from the cup was the ball at t=5 seconds?
d.
What was the speed of the ball as it moved towards the cup?
e.
What happened at t=7 seconds?
0Answer
meters/second;
it is
moving
yet
not available
in not
online
sample.
2Answer
metersnot available in online sample.
d
= 5 m;not
t =available
5s
v = sample.
d/t = 5 m / 5 s = 1 m/s
Answer
in online
Answer
available
online sample.
the
ball not
reached
the in
cup
4.
Two bicyclists are riding toward each other, and
each has an average speed of 10.0 km/h. When
their bikes are 20.0 km apart, a pesky fly begins
flying from one wheel to the other at a steady speed
of 30.0 km/h. When the fly gets to the wheel, it
abruptly turns around and flies back to touch the
first wheel, then turns around and keeps repeating
the back-and-forth trip until the bikes meet, and the
fly meets an unfortunate end.
How many kilometers did the fly travel in its total
back-and-forth trips?
The
dflyanswer
= ? is not available indthis
vflytfly =sample.
(30 km/h)(1 h) = 30.0 km
fly = online
vfly = 30.0 km/h
dbicycle = 10.0 km
vbicycle = 10.0 km/h
tfly = tbicycle = dbicycle/vbicycle = 10 km / 10 km/h = 1 h
There are several variants to solving this problem; consider having
students show their differing solutions on the board.
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
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UNIT 1: MOTION Lab: Galilean Ramp, pages 4-5
Expansion of the Idea (continued)
After W orksheet A, the next step is to clarify the speed concept and introduce acceleration.
Tell the students they are now going to explore the question, "How is the speed of the ball/cart changing?"
In other words, they are going to discover exactly how the speed was rising.
Instruct the students to calculate the speed on each run on their lab and record the results in the shaded
rightm ost colum n of the lab's data table. Then have them graph speed vs. tim e.
Computer Graphing:
If using a com puter to form the graph, you m ight be able to pre-load the fourth and final page of the lab
into the printer so that questions 8-12 appear below the printed graph. Again, check during the approval
process that they have plotted (0,0) and engage them in a discussion if it is m issing.
Students m ay have a tendency to select a quadratic fit with the parabola opening along the x-axis; this is
due to friction. It is crucial that a linear fit be selected, so m onitor their graphing and guide them to see
how a linear fit has little, if any, m ore error than a quadratic fit, so the sim pler linear fit should be selected.
Hand Graphing:
Since this data is linear, it should be no great challenge to hand-draw the graph and draw a best-fit line.
You should point out to students that a best-fit line need not hit any of the data points nor go through the
origin; the best-fit line sim ply runs through the “m iddle” of the data points as plotted. The students can
then determ ine the slope and y-intercept of their best-fit line.
After the second graph is m ade and analyzed, the students are given a brief overview of the types of error
in an experim ent and asked to discuss the system atic error in their experim ent.
Sam ple answers for those final pages follow.
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
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UNIT 1: MOTION Lab: Galilean Ramp, pages 4-5
answer all questions in complete sentences, except for math formulas
8.
What kind of fit (linear, quadractic, inverse, etc.) did you perform on the above speed vs. time graph?
We selected a linear fit.
9.
What does this graph indicate about the relationship between speed and time?
Answer
availableproportional
in this online to
sample.
Speednot
is directly
time.
10. Express the relationship you described in question 9 as a proportionality:
v%t
11. How was the speed changing as the ball/cart went down the track?
The
speed
steadily
Answer
not is
available
inincreasing.
online sample.
12. Your graph allows you to formulate an equation that fits your data. Write that equation below, substituting the appropriate variable
letters for x and y, and rounding off the numbers to the proper significant figures.
v = 6.93not
t + available
2.07
Answer
in online sample.
Em phasize when discussing this graph with the students how the linear graph indicates how the speed is
changing; they should be able to be m ore specific than sim ply saying the speed is rising. Soon you will
lead them to realize that the slope of the graph is related to (but not equal to) the acceleration (but they
m ust first realize that they were graphing average speed, not instantaneous speed, versus tim e here).
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
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UNIT 1: MOTION Lab: Galilean Ramp, pages 4-5
Types of Laboratory Error
Type
Examples
Prevention
Discussion
personal error
(mistakes)
mis-reading a scale
or incorrectly rearranging an
equation or calculating a
figure
check against lab partners’
work; redo parts of lab as
needed when error
discovered
none; should be corrected
before lab is submitted
systematic error
miscalibration or
uncontrolled variables
(e.g. friction); includes
unavoidable timing errors
calibrate equipment when
possible; think through
procedures to minimize
error
identify any uncontrollable
variables
(do not include variables
causing random error)
random error
estimating the last digit on a
scale reading; minor
variations in temperature or
air pressure
eliminate when possible;
can never be completely
eliminated
none
13.
In a few sentences, discuss the systematic error in this laboratory.
Answer not available
in online
sample.
Systematic
error would
include
timing error due to human reaction
time in triggering the stopwatch as well as releasing the ball,
error due to friction on the track, and error caused by imperfections
of the track surface.
In discussing the lab before it is subm itted, stress to students that a generic statem ent that there was
“hum an error” will not suffice. Som e hum an error is random , such as trying to place the ball correctly at
the starting m ark or in reading the m eterstick to m ake the m arks along the track. That error should not be
discussed. But hum an reaction tim e is usually a system atic error in that there is a delay in the triggering
and releasing of the ball. They need to m ake this clear in their discussion.
The tracks you use m ay also have obvious im perfections, such as a bowed track, knotholes in a wooden
track, etc. These again system atically bias the data and thus should be discussed. Som etim es students
m ay find their ball just sits there on a wooden track after release. Obviously that is a system atic error
worth noting. The solution one m ight em ploy for this dilem m a is m oving that starting m ark a few
centim eters to get away from the surface im perfection, and altering the data table and graph accordingly.
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
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UNIT 1: MOTION Lab: Galilean Ramp, pages 4-5
Using the second graph to develop concepts of average speed, instantaneous speed, and acceleration:
After you have discussed the second graph and its interpretation with the students, you need to develop
the concepts of average speed and acceleration.
A Provocative Question for the Class:
W here along the track did the speed you calculated occur? In other words, where along a
given run was the ball/cart rolling at the speed you calculated – at the beginning, m iddle,
end? (Don't use this term inology yet, but you are asking them at what position the
average speed and instantaneous speed were equal.)
Few students will give the correct answer, that the ball/cart was rolling at the calculated speed when it was
1/4 of the way down the track from its starting point. Lead the class to consider their speed vs. tim e graph
and observe that distance over tim e m ust yield an average speed that occurs at the halfway point in tim e.
Som e will then see that the average speed equaled the instantaneous speed 1/4 of the way down a given
run.
But you m ust m ake this concrete. So set up a run on a track on your dem o desk and pass out som e
stopwatches. Have the students yell out when half of the tim e has elapsed so that the students can see
where the ball/cart is located when it is m oving at its "average" speed.
Now they should be satisfied that d/t yields average speed, and not the speed at an instant. Have them
correct their notes (this will get their attention!) and insert a bar over the v in v=d/t. You can now also use
their speed vs. tim e graph to show that the average could also be calculated by taking the highest and
lowest speed on the graph, adding them together, and dividing by two. (The graph is linear, so you are
finding the m idpoint, which is the average speed.) This yields their second equation for the
year:
Now, you are really playing a gam e here, since you are finding the average speed on a graph of average
speed vs. tim e! You need not point this out to the students if it gets too confusing.
Next, have them consider the slope of their v vs. t graph and how it shows how the speed changes with
tim e. In other words, it shows the acceleration of the ball/cart. Let a student com e up with the term
acceleration here; one is bound to think of it. You can then quickly lead them to:
Discuss the units of acceleration (m /s2 , m i/h2 , (m i/h)/s, etc.) and also have them note that the acceleration
equation can be algebraically m anipulated to predict final speed:
Point out how the best-fit linear equation of the speed vs. tim e graph m atches this form at (the acceleration
is the slope, and the y-intercept is the initial speed). They will note that v i is not com ing out zero, which
can be attributed to experim ental error. You m ay (or m ay not) wish to point out that their slope is not really
the acceleration, since they are graphing average speed vs. tim e and not instantaneous speed vs. tim e.
Em phasize how the slope of a distance vs. tim e graph is speed, while the slope of a speed vs. tim e graph
is acceleration.
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
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P AG E 13 O F 18
UNIT 1: MOTION Worksheet B: Interpreting Motion Graphs
You need to prepare students before giving them W orksheet B. You will be teaching them to interpret
graphs of one-dim ensional forward m otion with positive or zero acceleration. W ait to cover graphs of
backwards m otion, slowing down, and so forth until after the students have assim ilated the vector
concepts in unit two, when negative slopes on a m otion graph will m ake m uch m ore sense to them .
Now is a good tim e to set up a m otion detector as a dem o or group activity and dem onstrate various
m otions with real-tim e graphing as you have the students set down into their notes the d, v, and a vs. t
graphs for a m otionless object, one m oving at a steady speed, one accelerating steadily, and one
speeding up with an ever-increasing acceleration. The students will then be ready for W orksheet B.
Don’t worry if you don’t have a m otion detector - here is how the students can be their own m otion
detectors:
“Kinesthetic Graphing” Exercise
[Unit 4 includes a version of this for horizontal and vertical velocity vs. time graphs with both
positive and negative slopes.]
Divide your students into several groups. Hand each group a card with a particular d vs. t,
v vs. t, or a vs. t graph on it, and a toy ball. (Large nerf balls work best.) Have them
decide how to m ove the Nerf ball to create the m otion on the graph.
Then have a person from each group present to the class the m otion they have decided
upon: he or she will m ake the ball m ove in the intended m otion, signaling to the class the
tim e when the graph should begin and end.
Have the students in the other groups individually or as a group sketch a graph of that
m otion, telling them the axes that are to be used (d, v, or a vs. tim e). You m ay want to
pick a student to sketch the corresponding graph on the board or overhead.
You and the students should expect m istakes. You’ll probably want to walk around the
room , glancing at the sketches or perhaps have the students hold up their sketches to
help you assess how the class is doing.
An easy way to create the cards for this exercise is to cut out shapes A-E from a copy of
W orksheet B and add various axis labels to them .
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
FO R
U N IT 1: M O TIO N
P AG E 14 O F 18
UNIT 1: MOTION Worksheet B: Interpreting Motion Graphs
Unit 1:Motion
Worksheet B: Interpreting Motion Graphs
answer questions 1 and 2 in complete sentences
1.
What does the slope of a distance vs. time graph indicate about an object’s motion?
Answer
Speed not available in online sample.
2.
What does the slope of a speed vs. time graph indicate about an object’s motion?
Acceleration
Answer
not available in online sample.
Questions 3 - 8 refer to the following generic graph shapes. Write the letter corresponding to the appropriate graph
in the blank at the left of each question.
N/A
C
3.
Which shape fits a distance vs. time graph of an object moving at constant (non-zero) speed?
B
4.
Which shape fits a speed vs. time graph of an object moving at constant (non-zero) speed?
A/B
5.
Which two shapes fit a distance vs. time graph of a motionless object?
A
6.
Which shape fits a speed vs. time graph of a motionless object?
D
7.
Which shape fits a distance vs. time graph of an object that is speeding up at a steady rate?
C
8.
Which shape fits a speed vs. time graph of an object that is speeding up at a steady rate?
C
9.
Which of the following units is equivalent to (meters per second) per second?
a)
m
b)
m/s
c)
m/s2
d)
m/s3
C
10.
Which of the following units correspond to the slope of a distance vs. time graph?
a)
m
b)
s
c)
m/s
d)
m/s2
C
11.
Which of the following units correspond to the slope of a speed vs. time graph?
a)
m/s
b)
m•s
c)
m/s2
d)
m2 /s2
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
FO R
U N IT 1: M O TIO N
P AG E 15 O F 18
UNIT 1: MOTION Worksheet B: Interpreting Motion Graphs
The table below gives distance and time data for a moving object. Notice the varying size of the time intervals as the distance rises in 20
cm increments.
Distance (m)
Time (s)
0
0
20
4.5
40
6.3
60
7.7
80
8.9
100
10
N/A
C
12.
Which of the following distance vs. time graphs corresponds to the table data?
N/A
C
13.
Which of the following descriptions matches the graph you selected in question 12?
a) A motionless object.
b) An object moving at a constant speed.
c) An object undergoing constant, positive acceleration.
d) An object undergoing constant, negative acceleration.
N/A
A
14.
Which of the following speed vs. time graphs corresponds to the table data?
N/A
C
15.
Which of the following descriptions matches the graph you selected in question 14?
a) A motionless object.
b) An object moving at a constant speed.
c) An object undergoing constant, positive acceleration.
d) An object undergoing constant, negative acceleration.
BEWARE:
16.
If your answers to questions 13 and 15 are different from each other, you are claiming that the same object
can have two distinct motions simultaneously. Ask yourself, “Is that reasonable?”
A woman walks away from a starting point in a straight line.
A distance vs. time graph for her motion is shown at right.
a.
Describe the woman's motion between 0 and 2
seconds.
Sheavailable
is accelerating.
Not
in online sample.
b.
Fill out the table below.
Time Interval
2 to 4 seconds
4 to 6 seconds
6 to 8 seconds
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
Woman's Speed (m/s)
3
Not available
in
0 sample.
online
1
FO R
U N IT 1: M O TIO N
P AG E 16 O F 18
UNIT 1: MOTION Worksheet C: Combining the Variables of Motion
Next you will have the students invent five additional m otion equations, for a total of eight equations they
can use in solving kinem atics problem s.
W orksheet C rem inds them of the three equations they have developed so far. W ork through the first
question with them , to arrive again at
, which they saw when you interpreted their speed
vs. tim e graphs.
Let them work in groups to derive the rem aining equations. Give them a hint that num ber 2 uses the
answer from num ber 1, 3 uses 2, 4 uses 3, BUT to derive equation 5 they'll need to start over with their
original three equations.
Eventually they will have found the answers, which you should lead them to rewrite into their standard
form s:
1.
2.
3.
4.
5.
(One way to arrive at #5 is to set the first two equations at the top of the page equal to one another and
substitute for t the rearrangem ent of a = (v f - v i) / t.)
It is vital that they note that equation #4 can only be used when the object starts from rest, and that #5 is
especially useful when tim e is unknown. W ork a couple of exam ples with them and then give them
W orksheet D.
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
FO R
U N IT 1: M O TIO N
P AG E 17 O F 18
UNIT 1: MOTION Worksheet D: 1-Dimensional Motion Problems
I've shown the answers that did not already appear on the handout. Note that it is im portant to insist that
students show their givens, equation, substituted num bers with units, and a boxed answer with proper
significant figures. Build good habits early on for showing all work.
Worksheet D: 1-Dimensional Motion Problems
1.
The head of a rattlesnake can accelerate 50.0 m/s2 in striking a victim. If a car could do as well, how long would it take for it
to reach a speed 24.6 m/s (which is about 55 mi/h) from rest?
2.
0.492 s
N/A
The speed limit on an 86.0 mile highway was changed from 55.0 mi/h to 75.0 mi/h. How much time was saved on the trip for
someone traveling at the legal speed limit?
0.417 h or 25.0 min or 1500 s
N/A
3.
In an emergency, a driver brings a car to a full stop in 5.00 seconds. The car is traveling along a highway at a rate of 24.6 m/s
when braking begins.
N/A
a.
At what rate is the car accelerated?
– 4.92 m/s2
b.
How far does it travel before stopping?
61.5
N/A m
4.
A supersonic jet flying at 200. m/s is accelerated uniformly at the rate of 23.1 m/s2 for 20.0 seconds.
a.
What is its final speed?
662
N/A m/s
b.
Physicist Ernst Mach studied the effects of motion faster than sound, and the ratio of a speed to that of sound is
called its “Mach number”. The speed of sound itself is 331 m/s (approx. 740 mi/h) at supersonic airplane altitudes.
“Mach 1.00" is the ratio 331/331, or the speed of sound. One of the fastest planes was the SR-71 Blackbird. It
flew at 1059 m/s, so 1059/331 = 3.20; we say it flew at “Mach 3.20.” What is the Mach speed of our jet?
Mach 2.00
N/A
5.
If a bullet leaves the muzzle of a rifle with a speed of 600. m/s, and the barrel of the rifle is 0.800 m long, at what rate is the
bullet accelerated while in the barrel? N/A
225,000 m/s2
6.
What is the acceleration of a racing car if its speed is increased uniformly from 44.0 m/s to 66.0 m/s over an 11.0 s period?
2.00
N/A m/s2
7.
An engineer is to design a runway to accommodate airplanes that must gain a ground speed of 360. km/h (approx. 225 mi/h)
before they can take off. These planes are capable of being accelerated uniformly at the rate of 3.60Г—104 km/h 2 .
a.
How many kilometers long must the runway be?
1.80
N/A km
b.
How many seconds will a plane need to accelerate to take-off speed?
36.0 s
N/A
8.
A plane flying at the speed of 150. m/s is accelerated uniformly at a rate of 5.00 m/s2 .
a.
What is the plane's speed at the end of 10.0 seconds?
N/A m/s2
200
b.
What distance has it traveled?
N/A m
1750
9.
A Tokyo express train is accelerated from rest at a constant rate of 1.00 m/s2 for 1.00 minute. How far does it travel during
this time?
1800
N/A m
10.
In a vacuum tube, an electron is accelerated uniformly from rest to a speed of 2.60Г—105 m/s during a time period of 6.50Г—10-2
N/A
seconds. Calculate the acceleration of the electron.
4.00Г—106 m/s2
IN Q U IRY P H YSICS T EACH ER 'S G U ID E
FO R
U N IT 1: M O TIO N
P AG E 18 O F 18
Equipment Suggestions for Unit 1: Motion
Equipment for each group (of 3 to 4 students):
Item
grooved wooden track OR air track OR other
dynamics track with ball or cart, about 1.5 to 2 m
long
if using a wooden track, a 7 mm groove should run
lengthwise along the track for a steel ball
(e.g. large ball bearing) to roll along; a wooden
block or other stop will be needed at the bottom of
the track
ring stand OR blocks to incline the track
ball for wooden track (diameter ≈ 2 cm and mass ≈
60 g) OR air track glider OR wheeled toy/cart
meter stick
stopwatch
Suggestions
I use wooden tracks made locally over two decades
ago, with ball bearings from oil field equipment.
You could use an air track and glider, available
from a variety of sources (we use Daedalon tracks
for other labs, but I like the simplicity of the ball on
the ramp for this first unit).
But if I were starting out, I’d consider buying lowfriction dynamics carts with tracks (which can act
as long inclined planes) from Pasco. They have
various accessories and integrate well with their
probeware.
I hate stopwatches with alarms and clocks and the
rest, greatly preferring MyChron stopwatches for
their simplicity and long battery life:
Sargent Welch item WLS77448
Science Kit item 46185M01
masking tape
Inquiry Physics: Equipment Suggestions
Page 1 of 2
EQUIPMENT SUGGESTIONS
for INQUIRY PHYSICS A Modified Learning Cycle Curriculum
The student handouts often avoid listing specific equipment so that you can be more flexible in your
approach. But here I have gathered a listing, current as of the summer of 2010, of the type of
equipment I use in each unit for the student labs as well as various demonstrations.
There are a number of nationally recognized science education supply houses which offer a vast array of
physics education equipment. Do not take their list prices at face value. Contact them about pricing
agreements where they might agree to offer a set discount or free shipping, etc. Here is a sampling:
GENERAL SCIENCE SUPPLIERS
SPECIALTY SUPPLIERS
Frey Scientific
www.freyscientific.com
School Specialty Frey Scientific
P.O. Box 3000
Nashua, NH 03061-3000
1-800-225-FREY (3739)
Fax: 1-877-256-FREY (3739)
Pasco Scientific
www.pasco.com
10101 Foothills Boulevard
Roseville, CA 95747
1-800-772-8700
Fax: 1-916-786-7565
Science Kit & Boreal Laboratories
www.sciencekit.com
P.O. Box 5003
Tonawanda, NY 14151-5003
1-800-828-7777
Fax: 1-800-828-FAXX (3299)
Vernier Software & Technology
www.vernier.com
13979 SW Millikan Way
Beaverton, OR 97005-2886
1-888-837-6437
Fax: 1-503-277-2440
Sargent-Welch
www.sargentwelch.com
P.O. Box 4130
Buffalo, NY 14217
1-800-727-4368
Fax: 1-800-676-2540
Nasco
http://www.enasco.com/
901 Janesville Avenue
P.O. Box 901
Fort Atkinson, WI 53538-0901
1-800-558-9595
Fax: 1-800-372-1236
Flinn Scientific
www.flinnsci.com
P.O. Box 219
Batavia, IL 60510
1-800-452-1261
Fax: 1-866-452-1436
Fisher Science Education
www.fishersci.com
4500 Turnberry Drive
Hanover Park, IL 60133
1-800-955-1177
Fax: 1-800-955-0740
Inquiry Physics: Equipment Suggestions
Design Simulation Technologies, Inc.
(Interactive Physics)
www.design-simulation.com
43311 Joy Road, #237
Canton, MI 48187
1-800-766-6615
1-734-259-4207
Edmund Scientific
http://scientificsonline.com
60 Pearce Ave
Tonawanda, NY 14150
1-800-728-6999
Fax: 1-800-828-3299
The Science Source
(Daedalon)
www.thesciencesource.com
299 Atlantic Highway
Waldoboro, ME 04572
1-800-299-5469
Fax: 1-207-832-7281
Page 2 of 2
INQUIRY PHYSICS
A Modified Learning Cycle Curriculum
by Granger Meador
Unit 1: Motion
Student Papers
inquiryphysics.org
2010
these SAMPLE NOTES, the STUDENT PAPERS, and any PRESENTATIONS for each unit have a creative
commons attribution non-commercial share-alike license; you may freely duplicate, modify, and
distribute them for non-commercial purposes if you give attribution to Granger Meador and reference
http://inquiryphysics.org
however, please note that the TEACHER’S GUIDES are copyrighted and all rights are reserved
so you may NOT distribute them or modified versions of them to others
1: Motion
Name
Lab: Galilean Ramp
There are fundamental principles governing the motion of all objects, from supersonic aircraft to
glaciers. This lab is similar to experiments conducted by Galileo Galilei several hundred years
ago which laid the foundations for modern-day physics.
Set up the equipment as shown in the diagram below:
Use the ring stand and ring to raise one end of the track until the distance between the bottom of
the track and the tabletop is 10.00 cm.
You will be varying distance. If necessary, mark off on masking tape the following distances
from the lower end of the track: 25.00 cm, 50.00 cm, 75.00 cm, 100.00 cm, 125.00 cm,
150.00 cm, and 175.00 cm. Be sure the tape will not interfere with the motion of the ball or cart.
You will measure the time required for the ball/cart to travel each of those seven distances.
1.
Begin taking data by placing the ball/cart at the 175.00 cm mark. To start the ball/cart the
same way each time, keep it at the mark on the incline with a pencil until you are ready to
release it and begin timing. Don't push or spin the ball/cart when you pull the pencil
away! Start a stopwatch as the ball/cart is released and stop the watch when it reaches the
stop. Make three measurements of time to as many decimal places as possible, ensuring
that the difference between the highest and lowest measurements is no more than 0.10 s.
Record those values in the table on the reverse.
2.
Gather the same data as before, but start the ball/cart at the mark that will make the
distance equal to 150.00 cm. Make three measurements of time and record them in the
table.
3.
Repeat the data gathering process for each of the other distances. Record the data in the
table.
Unit 1: Motion, Lab: Galilean Ramp
Page 1 of 5
©2010 by G. Meador – www.inquiryphysics.org
Distance (cm)
Time (s)
Average Time (s)
175.00
150.00
125.00
100.00
75.00
50.00
25.00
The Idea answer all questions in complete sentences
1.
Identify the independent and dependent variables in this experiment.
Create a graph of distance traveled along the incline versus average time. Graphs involving time always plot time
horizontally on the x-axis and the other variable vertically on the y-axis. This can violate the usual practice of placing the
independent variable on the x-axis and the dependent on the y-axis.
You need to decide if (0,0) is a valid point to include. Make sure each member of the group has a graph.
2.
W hat is the shape of the line on your graph? (Is it straight or is it curved? If it is curved, state whether it looks
parabolic or hyperbolic, etc.)
3.
The shape of a graph illustrates the mathematical relationship between the independent and dependent variables.
W hat does your graph specifically show you about the relationship between distance and time?
4.
Express the relationship you described in question 3 as a proportionality:
5.
According to the graph, what was the ball/cart doing as it went down the track?
Unit 1: Motion, Lab: Galilean Ramp
Page 2 of 5
©2010 by G. Meador – www.inquiryphysics.org
6.
Apply a best-fit curve to your graph. What type of fit did you perform, or instruct the computer
or calculator to perform (linear, quadratic, inverse, etc.)?
7.
In question 4, you expressed the basic proportionality between the independent and dependent
variables. Your best-fit curve allows you to now express the precise equation for your group's
data. Use your graph to fill in the missing values in this equation. Round off the values to the
appropriate number of significant figures.
d = ________ + ________ t + ________ t2
Soon we will examine how the speed of the ball/cart was changing.
Unit 1: Motion, Lab: Galilean Ramp
Page 3 of 5
©2010 by G. Meador – www.inquiryphysics.org
answer all questions in complete sentences, except for math formulas
8.
What kind of fit (linear, quadratic, inverse, etc.) did you perform on the speed vs. time graph?
9.
What does this graph indicate about the relationship between speed and time?
10.
Express the relationship you described in question 9 as a proportionality:
11.
How was the speed changing as the ball/cart went down the track?
12.
Your graph allows you to formulate an equation that fits your data. Write that equation below,
substituting the appropriate variable letters for x and y, and rounding off the numbers to the
proper significant figures.
Unit 1: Motion, Lab: Galilean Ramp
Page 4 of 5
©2010 by G. Meador – www.inquiryphysics.org
Types of Laboratory Error
Type
Examples
Prevention
Discussion
personal error
(mistakes)
mis-reading a scale
or incorrectly
rearranging an
equation or
calculating a figure
check against lab
partners’ work; redo
parts of lab as
needed when error
discovered
none; should be
corrected before lab
is submitted
systematic error
miscalibration or
uncontrolled
variables
(e.g. friction);
includes unavoidable
timing errors
calibrate equipment
when possible; think
through procedures
to minimize error
identify any
uncontrollable
variables
(do not include
variables causing
random error)
random error
estimating the last
digit on a scale
reading; minor
variations in
temperature or air
pressure
eliminate when
possible; can never
be completely
eliminated
none
13.
In a few sentences, discuss the systematic error in this laboratory.
Unit 1: Motion, Lab: Galilean Ramp
Page 5 of 5
©2010 by G. Meador – www.inquiryphysics.org
1: Motion
Name
Worksheet A: Calculating Motion
1.
2.
The Spirit and Opportunity robot rovers landed on Mars in 2004 and explored its surface
for years. The rovers’ spacecraft and the rovers themselves travelled at wildly different
speeds.
a.
The Spirit rover could move across the Martian
landscape at a maximum of 2.68 m/min. How
many minutes would it take for it to travel
10.4 m, the length of a typical classroom?
2.
Spirit journeyed to Mars in a spacecraft that
traveled about 487 gigameters (487Г—109 m or
303 million miles) from Earth to Mars,
averaging about 27,100 m/s (60,600 mi/h). Use
the SI units to calculate how many Earth days it
took for the spacecraft to complete its journey.
A runner in a 1.00Г—102 meter race passes the 40.0 meter mark with a speed of 5.00 m/s.
a.
If she maintains that speed, how far from the starting line will she be
3.00 seconds later?
b.
If 5.00 m/s was her top speed, what is the shortest possible time for her entire
1.00Г—102 m run?
CONTINUED...
Unit 1: Motion, Worksheet A: Calculating Motion
©2010 by G. Meador – www.inquiryphysics.org
3.
4.
The graph above describes the motion of a golf ball. Note that it graphs distance from a
position, not distance traveled. The ball is placed on the green at 5 meters from the cup
at t=0 seconds.
a.
How far from the cup was the ball at t = 1 second?
b.
What was the speed of the ball at t = 1 second?
c.
How far from the cup was the ball at t = 5 seconds?
d.
What was the speed of the ball as it moved towards the cup?
e.
What happened at t = 7 seconds?
Two bicyclists are riding toward each
other, and each has an average speed of
10.0 km/h. When their bikes are
20.0 km apart, a pesky fly begins flying
from one wheel to the other at a steady
speed of 30.0 km/h. When the fly gets
to the wheel, it abruptly turns around
and flies back to touch the first wheel,
then turns around and keeps repeating
the back-and-forth trip until the bikes
meet, and the fly meets an unfortunate end.
How many kilometers did the fly travel in its total back-and-forth trips?
Unit 1: Motion, Worksheet A: Calculating Motion
©2010 by G. Meador – www.inquiryphysics.org
1: Motion
Name
W orksheet B: Interpreting Motion Graphs
answer questions 1 and 2 in complete sentences
1.
W hat does the slope of a distance vs. time graph indicate about an object’s motion?
2.
W hat does the slope of a speed vs. time graph indicate about an object’s motion?
Questions 3 - 8 refer to the following generic graph shapes. W rite the letter corresponding to the
appropriate graph in the blank at the left of each question.
3.
W hich shape fits a distance vs. time graph of an object moving at constant (non-zero) speed?
4.
W hich shape fits a speed vs. time graph of an object moving at constant (non-zero) speed?
5.
W hich two shapes fit a distance vs. time graph of a motionless object?
6.
W hich shape fits a speed vs. time graph of a motionless object?
7.
W hich shape fits a distance vs. time graph of an object that is speeding up at a steady rate?
8.
W hich shape fits a speed vs. time graph of an object that is speeding up at a steady rate?
9.
W hich of the following units is equivalent to (meters per second) per second?
a) m
b) m/s
c) m/s 2
10.
11.
d)
m/s 3
W hich of the following units correspond to the slope of a distance vs. time graph?
a) m
b) s
c) m/s
d)
m/s 2
W hich of the following units correspond to the slope of a speed vs. time graph?
a) m/s
b) m•s
c) m/s 2
d)
m 2/s 2
CONTINUED ...
Unit 1: Motion, Worksheet B: Interpreting Motion Graphs
©2010 by G. Meador – www.inquiryphysics.org
The table below gives distance and time data for a moving object. Notice the varying size of the time intervals as the distance
rises in 20 cm increments.
Distance (m)
Time (s)
0
0
20
4.5
40
6.3
60
7.7
80
8.9
100
10
12.
W hich of the following distance vs. time graphs corresponds to the table data?
13.
W hich of the following descriptions matches the graph you selected in question 12?
a) A motionless object.
b) An object moving at a constant speed.
c) An object undergoing constant, positive acceleration.
d) An object undergoing constant, negative acceleration.
14.
W hich of the following speed vs. time graphs corresponds to the table data?
15.
W hich of the following descriptions matches the graph you selected in question 14?
a) A motionless object.
b) An object moving at a constant speed.
c) An object undergoing constant, positive acceleration.
d) An object undergoing constant, negative acceleration.
If your answers to questions 13 and 15 are different from each other, you are claiming that the same object
can have two distinct motions simultaneously. Ask yourself, “Is that reasonable?”
BEW ARE:
16.
A woman walks away from a starting point in a straight line.
A distance vs. time graph for her motion is shown at right.
a.
Describe the woman's motion between 0 and 2 seconds.
b.
Fill out the table below.
Time Interval
W oman's Speed (m/s)
2 to 4 seconds
4 to 6 seconds
6 to 8 seconds
Unit 1: Motion, Worksheet B: Interpreting Motion Graphs
©2010 by G. Meador – www.inquiryphysics.org
1: Motion
Name
Worksheet C: Combining the Variables of Motion
We have already developed three equations for velocity and acceleration:
Using these equations, figure out ways to combine them algebraically to make five other
equations that would enable you to:
1.
Solve for vf when you know vi, a, and t.
2.
Solve for d when you know vi, a, and t.
3.
Solve for a when you know vi, d, and t.
4.
Solve for t when you know d and a, and vi=0.
5.
Solve for vf when you know vi, a, and d.
Unit 1: Motion, Worksheet C: Combining the Variables of Motion
©2010 by G. Meador – www.inquiryphysics.org
1: Motion
Name
W orksheet D: 1-Dim ensional Motion Problem s
2
1.
The head of a rattlesnake can accelerate 50.0 m/s in striking a victim. If a car could do as well, how long
would it take for it to reach a speed 24.6 m/s (which is about 55 mi/h) from rest?
0.492 s
2.
The speed limit on an 86.0 mile highway was changed from 55.0 mi/h to 75.0 mi/h. How much time was
saved on the trip for someone traveling at the speed limit?
0.417 h
3.
In an emergency, a driver brings a car to a full stop in 5.00 seconds. The car is traveling along a highway at
a rate of 24.6 m/s when braking begins.
2
a.
At what rate is the car accelerated?
– 4.92 m/s
b.
4.
2
A supersonic jet flying at 200. m/s is accelerated uniformly at the rate of 23.1 m/s for 20.0 seconds.
a.
W hat is its final speed?
b.
5.
How far does it travel before stopping?
Physicist Ernst Mach studied the effects of motion faster than sound, and the ratio of a speed to
that of sound is called its “Mach number”. The speed of sound itself is 331 m/s (approx. 740 mi/h)
at supersonic airplane altitudes. “Mach 1.00" is the ratio 331/331, or the speed of sound. One of
the fastest planes was the SR-71 Blackbird. It flew at 1059 m/s, so 1059/331 = 3.20; we say it flew
at “Mach 3.20.” W hat is the Mach speed of our jet?
If a bullet leaves the muzzle of a rifle with a speed of 600. m/s, and the barrel of the rifle is 0.800 m long, at
what rate is the bullet accelerated while in the barrel?
2
225,000 m/s
Unit 1: Motion, Worksheet D: 1-Dimensional Motion Problems
©2010 by G. Meador – www.inquiryphysics.org
6.
W hat is the acceleration of a racing car if its speed is increased uniformly from 44.0 m/s to 66.0 m/s over an
11.0 s period?
7.
An engineer is to design a runway to accommodate airplanes that must gain a ground speed of 360. km/h
(approx. 225 mi/h) before they can take off. These planes are capable of being accelerated uniformly at the
2
rate of 3.60Г—10 4 km/h .
a.
How many kilometers long must the runway be?
b.
8.
How many seconds will a plane need to accelerate to take-off speed?
2
A plane flying at the speed of 150. m/s is accelerated uniformly at a rate of 5.00 m/s .
a.
W hat is the plane's speed at the end of 10.0 seconds?
b.
W hat distance has it traveled?
2
9.
A Tokyo express train is accelerated from rest at a constant rate of 1.00 m/s for 1.00 minute. How far
does it travel during this time?
10.
In a vacuum tube, an electron is accelerated uniformly from rest to a speed of 2.60Г—10 m/s during a time
-2
period of 6.50Г—10 seconds. Calculate the acceleration of the electron.
6
4.00Г—10 m/s 2
Unit 1: Motion, Worksheet D: 1-Dimensional Motion Problems
5
©2010 by G. Meador – www.inquiryphysics.org
1 Motion
Name
W orksheet E: Quiz Practice Problem s
1.
A fly takes off with an acceleration of 0.700 m/s2 from a wall. How many seconds will it take the fly to reach a
speed of 12.6 km/h?
2.
In
a.
b.
c.
3.
The evil Victor Vector has tied poor Velma Velocity to a train track. He is aboard a train which is moving at
5.00 m/s when it is 175 m from the struggling Velma. If the train is accelerating at 3.00 m/s2, how much time
does she have to make her escape?
4.
The Hanson brothers are backstage after a concert, sauntering at 0.500 m/s, when a horde of screaming fans
gives chase. The musicians are 12.0 m away from the safety of their dressing room. If they accelerate steadily
and reach the room in 3.20 s, how fast are they traveling as they pass its doorway?
5.
Mr. M is a human cannonball in his spare time. If the cannon he uses is 1.75 meters long and he exits the
cannon at a speed of 20.0 m/s, what acceleration does the cannon impart to Mr. M?
the graph:
W hat is the speed and acceleration from 0 to 1 seconds?
W hat is the speed and acceleration from 1 to 3 seconds?
W hat is the acceleration from 3 to 5 seconds?
(assume it is constant)
d. W hat is the object doing from 5 to 7 seconds?
Unit 1: Motion, Worksheet E: Quiz Practice Problems
©2010 by G. Meador – www.inquiryphysics.org
Unit 1: Motion Notes
Meador’s Inquiry Physics
Page 1 of 7
INQUIRY PHYSICS
A Modified Learning Cycle Curriculum
by Granger Meador
Unit 1: Motion
Sample Notes
I recommend that you always write out notes,
by hand, on the board for each class. That
allows you to control the pacing and focus,
rather than having students ignore you while
they simply copy down the content of a slide. It
also controls your pacing, so that you don’t race
ahead but instead focus on student
understanding.
Unit 1 focuses on development
and use of one-dimensional
motion equations.
inquiryphysics.org
2010
these SAMPLE NOTES, the STUDENT PAPERS, and
any PRESENTATIONS for each unit have a creative
commons attribution non-commercial share-alike
license; you may freely duplicate, modify, and
distribute them for non-commercial purposes if
you give attribution to Granger Meador and
reference http://inquiryphysics.org
Ask frequent questions of students to check
their grasp of the material, and call upon
students to provide the next step when working
examples.
My rule for students is that if I write it on the
board, they must write it in their notes, and I
grade their notes each quarter and take off for
any units with incomplete notes or examples.
Trigonometry-Based Physics
(AP Physics B)
These notes apply to both algebra-based
Inquiry Physics and to trigonometry-based
physics. Trig concepts will not be introduced
until Unit 2 on Vectors.
however, please note that the TEACHER’S GUIDES are copyrighted and all rights are reserved
so you may NOT distribute them or modified versions of them to others
Unit 1: Motion Notes
Meador’s Inquiry Physics
Page 2 of 7
Sample Notes for Unit 1: Motion
Unit 1: Motion
speed = distance / time
UNITS: mi/h, km/h, m/s, furlongs/fortnight, etc.
meter = distance light travels in
s
second = defined by vibrations of gas atoms in atomic
clocks
PROBLEM-SOLVING PROCEDURES
1.
Write down the givens
2.
Show the equation used in original form
3.
Show all work, with units
4.
Answer must have proper significant figures,
units, and be boxed
These notes begin after the students have
completed the first three pages of the Unit
1 lab. They’ve thus seen that distance is
directly proportional to the square of time,
and that means the ball was speeding up.
So we begin by formally defining those
quantities.
Note that we do NOT yet distinguish
between average and instantaneous speed.
That comes after the next part of the lab.
I am very strict with students about these
procedures. While I seldom grade on their
givens, I take off 2 points for a missing
equation, 1 point off for any missing units
in their calculations or answer, 1 point off
for wrong significant figures in the answer,
and award little if any credit unless all
work is shown.
“All work” means they have to show the
plugging in of values from their givens,
with units, into their equation. They can
then optionally show more work as
intermediate steps to the answer.
I stress to students that this is how they get
partial credit on their work and ensure it is
decipherable by both me and by them,
including a year or more from now when
they use this in college.
Unit 1: Motion Notes
Meador’s Inquiry Physics
Example 1-1
Phluffy the cat was being chased by a lawnmower. She
travelled 10.0 m at 4.00 m/s.
a) What was her time of travel?
v = 4 m/s
d = 10.0 m
t=?
Page 3 of 7
I indicate common errors as I work this
example and how many points they would
lose. In my scheme, part “a” might be
worth 6 points. I’d take off 1 pt. for a
wrong or missing equation, 1 pt. for wrong
or missing units, 1 pt. for not having 3 sig
figs in the answer, and 3 points for a
math/algebra error (such as t=dv). So
they could make the algebra mistake and
still get half credit if their work allowed us
both to see that the algebraic
rearrangement was where things went
awry. But they could also lose half of the
credit through careless notational errors.
b) What was her speed in furlongs/fortnight?
4
m
s
100
cm
m
in
ft
yd
furlong
3600 s
24 h
14 day
2.54
cm
12
in
3 ft
220 yd
h
day
ftnight
= 24,051.53901 furlongs/fortnight
Part “b” demonstrates unit conversions. I
insist they know how to do this, although I
will accept work where their calculator
made the conversion. I warn them that if
they have to borrow a calculator from me,
it won’t do those unit conversions.
=
c) Phluffy hit a wall and stopped in 25.0 Ојs. How far did
she travel while slamming to a halt?
v = 4 m/s
t = 25 Ојs = 25 x 10-6 s
d=?
d = vt = (4 m/s)(25 x 10-6 s) = 100. x 10-6 m
=
or
or
Next I assign Unit 1: Worksheet A.
The next day I walk to each student, assigning points for the number of problems completed,
even if they are wrong, and not yet taking off for notational errors. The focus is on them
showing work, and I personally point out to them repetitive mistakes he or she has made, such
as not showing equations or units or sig figs.
Then I go over the worksheet with them on an overhead projector or document camera,
pointing out how I showed my work. The final fly problem gives some of them fits, especially in
how to show their work. As I walked around the room, I had noted successful solutions to the fly
problem using various methods, and I call upon those students to work it on the board.
Unit 1: Motion Notes
Meador’s Inquiry Physics
Page 4 of 7
The next task is to have the students calculate the speeds on the lab, filling in that last column,
and then constructing graphs to determine how the speed was changing as the ball went down
the ramp. They quickly figure out to graph speed on the y-axis and time on the x, and they use it
to complete the lab.
When I go over that part of the lab with them, I check that they are seeing how the speed was
steadily increasing as time went by. This sets up the disequilibration of what speed really
means.
I put a track on the demo desk, marking with tape the Вј, ВЅ , Вѕ and full length of a run. I ask
them to discuss in their groups this question:
“Where along the track was the ball going the speed you indicated in the table?”
I then have them vote by hand on where they think that speed occurred. Few will correctly
indicate it was Вј of the way down from the starting point. Instead, most will say it occurred at
the halfway point, or Вѕ point, or at the end of the track.
That lets me then have them consider what distance/time really means. They eventually see
that it gives average speed, while my question was about an instantaneous speed. Once they
grasp that, I use their linear v vs. t graph to identify that the average speed in the table must
have occurred halfway along a run in time, not distance. And then we look on the parabolic d vs.
t graph for where a ball is halfway along a run in time…and it is only ¼ of the way along its
journey.
To prove the point, I hand out a stop watch to each group. The timers time how long a full run
of the ball down my demo desk track takes. Then we cut that in half, and they are to yell out as
soon as that much time elapses. Everyone else keeps their eye on the ball. They’ll see that the
timers yell out when the ball has not yet even reached the halfway point. (Reaction time delay
means they won’t yell out precisely when it is ¼ of the way along the journey.)
That is the setup for the next part of the notes. First we go back and “fix” the earlier speed
equation, adding a bar over the v to indicate that d/t yields average speed. And we use the
linear v vs. t graph to understand that average speed is also calculated by simply adding the
initial and final instantaneous speeds together and then dividing by two.
Unit 1: Motion Notes
Meador’s Inquiry Physics
Page 5 of 7
Average vs. Instantaneous Speed
yields average speed, . So
where vi = initial speed and vf = final speed
and vi and vf are the speeds at a given instant, or instantaneous speeds.
In the lab the ball was speeding up steadily, so its average speed occurred halfway along the journey in
time:
Graph Slopes
The slope of a distance vs. time graph is the object’s speed.
The slope of a speed vs. time graph is the object’s acceleration.
In our lab the speed increased steadily, so the acceleration was
constant.
acceleration = rate of speed change;
UNITS: m/s
2
, mi/h2, (mi/h)/s, etc.
Now it is time to introduce the concept of
the meaning of the slope of each graph and
the concept of acceleration. Some students
will have already used the term in the lab.
Unit 1: Motion Notes
Meador’s Inquiry Physics
Page 6 of 7
Graphs of 1-d Motion
I call upon a different
student to help me
draw each of these
graphs, thus hitting at
least 12 students
during the lecture.
I can hit another 8
students by repeatedly
asking them what the
slope of each graph
shape is and what we
call that slope. For
example, the slope of d
vs. t in the steady
speed case is a
constant positive
number, so the object
has a constant positive
speed. (That will get a
few students thinking
about what a negative
slope would mean, and
the golf ball graph on
Worksheet A can be a
resource for seeing
how it indicates
whether the object is
moving toward or
away from you.)
By the way, the name
for the slope of an
acceleration vs. time
graph is the “jerk”.
After these notes I assign Worksheet B on
graphs.
After that they do Worksheet C, using
algebra to create five new equations from
the existing three equations we have in the
notes.
That sets the stage for the final examples.
For the final set of
graphs, I ask all of the
students to sketch all
three graphs, looking
for a pattern in the
data. Most will spot
how the graph shapes
are shifting to the
right as you work
down the page.
The final d vs. t graph
has a steeper cubic
shape, not a quadratic
or parabolic one.
Unit 1: Motion Notes
Meador’s Inquiry Physics
Example 1-2
Phluffy accelerates from 2.50 m/s to 7.00 m/s over 16.0 m.
How much time did this take?
Page 7 of 7
I skip example 1-2 in my trigbased AP Physics B class, so
example 1-3 shown here becomes
example 1-2 in that course.
vi = 2.5 m/s
vf = 7 m/s
d = 16 m
t=?
so thus
t = 3.37 s
Example 1-3 (example 1-2 in AP Physics B)
Phyllis Physics was driving at 90.0 km/h (55 mi/h) when a cat jumped out in the road 40.0 m in
front of her car. Phyllis hesitated 0.750 s before braking at –10.0 m/s2. Did she hit the cat?
COASTING
BRAKING
t = 0.75 s
d=?
a = –10.0 m/s2
vi = 25 m/s
vf = 0
d=?
so
vf2 = vi2 + 2ad so
d = 31.25 m
dtotal = dcoasting + dbraking = 18.75 m + 31.25 m = 50.0 m
Yes; 50.0 m > 40.0 m
Alternatively one can set the total distance to be 40 m and solve for final speed. It will be positive,
meaning the car is still moving and the cat is hit. This problem is based on an incident that happened to
me near the Crazy Horse monument in South Dakota; happily the cat used up 1 of its 9 lives and survived.
I follow this with Worksheet D, then create and administer a quiz over Unit 1.