Unit 3 Constant Acceleration Essential Standards Curriculum Assistance Document 2013
Essential Standards
Phys 1.1 Analyze motion of objects
Unit
Constant Acceleration
Time Allowed
8
days
Concepts
Instantaneous vs. average velocity; slope of tangent on x vs t graph, slope and area under the curve
on v vs t graph, area under curve on a vs t graph; acceleration as vector
Vocabulary
Instantaneous velocity, average velocity, acceleration
a = ∆v/∆t v = v
o
+ at v
f
= v
i
+a∆t x
f
= x
i
+
v
i
∆
t
+ ½ a∆t
2
v
2
f
= v
2
i
+2a∆x
Lab/Activities
Inclined Rail/Ramp Lab
: acceleration analysis;
Unit 3 Worksheet 1
;
Unit 3 Worksheet 2
;
Unit 3: Stacks of Kinematic Curves
;
Unit 3 Worksheet 3
.
;
Unit 3 Worksheet 4
;
Match A Graph
Resources
Moving Man:
http://phet.colorado.edu/en/simulation/moving

man
;
Car acceleration:
http://www.walter

fendt.de/ph14e/acceleration.htm
Graph Matching:
http://mste.illinois.edu/courses/summer99/300tcd_1/mickley/Graphmatching.htm
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Lab Notes: Inclined Rail M
otion
Apparatus
High Tech.
Pasco dynamics carts and tracks or large steel ball
photogates (2)
Computer and ULI interface
ULI Timer (software for Macintosh)
Graphical Analysis
Low Tech.
Bowling ball, chalk and accessibility ramp or
disc and axle and
parallel

pipe ramp
Stopwatch, water clock, metronome or pendulum
Ticker tape, masking tape and markers
Graphical Analysis
Pre

lab discussion
•
Let a ball roll down an inclined rail and ask students for observations. Record all observations. To
proceed
, they must mention something to the effect that the ball speeds up as it rolls down.
•
To obtain a finer description, ask students which observations are measurable. Make sure they include
the observation that the ball speeds up as it rolls down the rail
. (Do not let them state the ball accelerates
since we haven't defined acceleration yet!)
•
Ask them how they can measure speed directly. Lead them to the conclusion that they cannot, but that
they can measure position and time.
•
Students should mark th
e position of the object at equal time intervals.
•
Time should be plotted as the independent variable.
Lab performance notes
•
A variety of constant acceleration motion such as a cart rolling down a track, a bowling ball rolling
down an access ramp, or
a disc and axle rolling down a ramp of two parallel pieces of conduit pipe.
•
Timing variations could include using photogates, water clocks, pendulums and metronomes in addition
to stopwatches.
•
Make sure that the angle of inclination is less than 30
o
.
•
Initial position and speed must be zero. (See sample graphs below.)
Time
Position
Position
Time
2
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UNIT III: Worksheet 1
When evaluating problems 1

3, please represent the motion that would result from the rail
configuration indicated by
means of a:
A) qualitative graphical representation of
x
vs.
t
B) qualitative graphical representation of
v
vs.
t
C) qualitative graphical representation of
a
vs.
t
D)
qualitative motion map
E) general mathematical expression of the
relationship between
x
and
t
F) general mathematical expression of the
relationship between
v
and
t
G) general mathematical expression of the
relationship between
a
and
t
D)
x
E) _____________________________
F) ____________________________
G)____________________________
t
t
v
t
a
x
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2)
D)
x
E) _____________________________
F) ____________________________
G)____________________________
t
t
v
t
a
x
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Name
Date
Pd
UNIT III: Worksheet 2
While cruising along a dark stretch of highway with the cruise control set 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 i
nstant you hit the
brakes.
1.
Construct a motion map that represents the motion described above, including position,
velocity, and acceleration. Clearly demonstrate how you can determine the direction (sign) of
the acceleration from the motion map represe
ntation.
2.
Construct
qualitative
graphical representations of the situation described above to illustrate:
a.
x
vs.
t
b.
v
vs.
t
c.
a
vs.
t
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3.
Construct a
quantitatively accurate
v
vs
t
graph to describe the situation.
4.
On the
v
vs
t
graph at right, graphically represent the car’s displacement during braking.
5.
Utilizing the
graphical representation
, determine how far the car traveled during braking.
(Please explain your problem solving method.)
6.
In order to draw the
a
v
s
t
graph, you need to
determine the car’s acceleration. Please do this, then
sketch a
quantitatively accurate
a
vs
t
graph
7.
Using the equation you developed for displacement of an accelerating object determine how
far the car traveled during
braking. (Please show your work.)
8.
Compare your answers to 5 and 7.
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Unit III: Stacks of kinematics curves
Given the following position vs time graphs, sketch the corresponding velocity vs time and
acceleration vs time graphs.
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For the following velocity vs time graphs, draw the corresponding position vs time and acceleration
vs time
graphs.
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Name
Date
Pd
UNIT III: Worksheet 3
1.
a.
Describe in words the motion of the
object from 0

6.0 s.
b.
Construct a qualitative motion map to describe the motion of the object depicted in the graph above.
c.
What is the instantaneous velocity of the object at the following times?
i.
t = 1.0 s
ii.
t = 3.0 s
d.
What is
the simple average of these two velocities?
What is the average velocity for the entire interval?
Why are these two values different? Which is best to describe the motion of the object?
x (m)
t (s)
0
5
25
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e.
Graphically represent the relationship between velocity and
time for the object described above.
f.
From your velocity vs. time graph determine the total displacement of the object.
2. The graph below represents the motion of an object.
a.
At what point(s) on the graph above is the object moving most slowly? (How do you know?)
b.
Over what intervals on the graph above is the object speeding up? (How do you know?)
c.
Over what intervals on the graph above is the
object slowing down? (How do you know?)
d.
At what point(s) on the graph above is the object changing direction? (How do you know?)
t (s)
0
v (m/s)
5
x
t
A
B
D
E
F
G
C
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3.
A stunt car driver testing the use of air bags drives a car at a constant speed of
25 m/s for a total of 100. m.
He
applies his brakes and accelerates uniformly to a stop just as he reaches a wall
50. m away.
a.
Sketch qualitative position vs. time and velocity vs time graphs.
b.
How long does it take for the car to travel the first 100.m?
c.
Remember that the
area under a velocity vs time graph equals the displacement of the car. How long
must the brakes be applied for the car to come to a stop in 50 m?
d.
Now that you know the total time of travel, sketch a
quantitative
velocity vs time graph.
e.
What
acceleration is provided by the brakes? How do you know?
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Name
Date
Pd
UNIT III: Worksheet 4
1.
A poorly tuned Geo Metro can accelerate from rest to a speed of
28 m/s in 20 s.
a) What is the average
acceleration of the car?
b) What distance does it travel in this time?
2.
At t = 0 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
bear spies some honey and takes off from rest, accelerating at a rate of 2.0 m/s
2
.
If the honey is 16 m away, how fast will his snout be going when it reaches the treat?
4.
A bus moving at 20 m/s (t = 0) 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?
v (m/s)
+

t (s)
v (m/s)
+

t (s)
v (m/s)
+

t (s)
v (m/s)
+

t (s)
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5.
A physics student skis down a hill, accelerating at a constant 2.0 m/s
2
.
If it takes her
15 s to reach the bottom, what is the length of the slope?
6.
A dog runs down his driveway with an initial speed of 5 m/s for 8 s, then uniformly increases his speed to
10 m/s in 5 s.
a)
What was his acceleration during
the 2nd part of the motion?
b)
How long is the driveway?
7.
A mountain goat starts a rock slide and the rocks crash down the slope 100 m.
If the rocks reach the bottom in 5 s, what is their acceleration?
8.
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 distance it travels in the 3rd second
(t = 2s to t = 3s).
v (m/s)
+

t (s)
v (m/s)
+

t (s)
v (m/s)
+

t (s)
v (m/s)
+

t (s)
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Graph Matching
One of the most effective methods of describing motion is to plot graphs of position, velocity, and acceleration
vs
. time. From such a graphical representation, it is possible to determine in what direction an object is going,
how fast it is moving, how fa
r it traveled, and whether it is speeding up or slowing down. In this experiment,
you will use a Motion Detector to determine this information by plotting a real time graph of
your
motion as
you move across the classroom.
The Motion Detector measures the t
ime it takes for a high frequency sound pulse to travel from the detector to
an object and back. Using this round

trip time and the speed of sound, you can determine the position to the
object. Logger
Pro
will perform this calculation for you. It can then
use the change in position to calculate the
object’s velocity and acceleration. All of this information can be displayed either as a table or a graph. A
qualitative analysis of the graphs of your motion will help you develop an understanding of the concept
s of
kinematics.
OBJECTIVES
Analyze the motion of a student walking across the room.
Predict, sketch, and test position
vs
. time kinematics graphs.
Predict, sketch, and test velocity
vs
. time kinematics graphs.
MATERIALS
computer
Vernier Motion Detector
Vernier computer interface
meter stick
Logger
Pro
masking tape
PRELIMINARY QUESTION
S
1.
Use a coordinate system with the origin at far left and positive positions increasing to the right. Sketch the
position
vs
. time graph for each of the following situati
ons:
An object at rest
An object moving in the positive direction with a constant speed
An object moving in the negative direction with a constant speed
An object that is accelerating in the positive direction, starting from rest
2.
Sketch the velocity
vs
.
time graph for each of the situations described above.
PROCEDURE
Part l Preliminary Experiments
1.
Connect the Motion Detector to the
DIG/SONIC 1
channel of the interface.
walk back and forth
in front of
Motion Detector
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2.
Place the Motion Detector so that it points toward an open space at least 4
m long.
Use short strips of
masking tape on the floor to mark the 1
m, 2
m, 3 m, and 4
m positions from the Motion Detector.
3.
Open the file “01a Graph Matching” from the
Physics with Computers
folder.
4.
Using Logger
Pro
, produce a graph of your motion when you walk a
way from the detector with constant
velocity. To do this, stand about 1
m from the Motion Detector and have your lab partner click
.
Walk slowly away from the Motion Detector when you hear it begin to click.
5.
Sketch what the position
vs.
time graph will lo
ok like if you walk faster. Check your prediction with the
Motion Detector.
6.
Try to match the shape of the position
vs
. time graphs that you sketched in the Preliminary Questions
section by walking in front of the Motion Detector.
Part Il Position
vs
. Time
Graph Matching
7.
Open the experiment file “01b Graph Matching.” A position
vs
. time graph will appear.
8.
Describe how you would walk to produce this target graph.
9.
To test your prediction, choose a starting position and stand at that point. Start data collecti
on by clicking
. When you hear the Motion Detector begin to click, walk in such a way that the graph of your
motion matches the target graph on the computer screen.
10.
If you were not successful, repeat the process until your motion closely matches the
graph on the screen. If a
printer is attached, print the graph with your best attempt.
11.
Open the experiment file “01c Graph Matching” and repeat Steps 8
–
10, using a new target graph.
12.
Answer the Analysis questions for Part II before proceeding to
Part III.
Part IIl Velocity
vs
. Time Graph Matching
13.
Open the experiment file “01d Graph Matching.” A velocity
vs
. time graph will appear.
14.
Describe how you would walk to produce this target graph.
15.
To test your prediction, choose a starting
position and stand at that point. Start by clicking
. When
you hear the Motion Detector begin to click, walk in such a way that the graph of your motion matches the
target graph on the screen. It will be more difficult to match the velocity graph than it
was for the position
graph.
16.
Open the experiment file “01e Graph Matching.” Repeat Steps 14
–
15 to match this graph.
17.
Remove the masking tape strips from the floor.
ANALYSIS
Part II Position
vs
. Time Graph Matching
1.
Describe how you walked for
each of the graphs that you matched.
2.
Explain the significance of the slope of a position
vs
. time graph. Include a discussion of positive and
negative slope.
3.
What type of motion is occurring when the slope of a position
vs
. time graph is zero?
4.
What type of
motion is occurring when the slope of a position
vs
. time graph is constant?
5.
What type of motion is occurring when the slope of a position
vs
. time graph is changing? Test your answer
to this question using the Motion Detector.
6.
Return to the procedure and
complete Part III.
Part III Velocity
vs
. Time Graph Matching
7.
Describe how you walked for each of the graphs that you matched.
8.
Using the velocity
vs
. time graphs, sketch the position
vs
. time graph for each of the graphs that you
matched. In Logger
Pro
, s
witch to a position
vs
. time graph to check your answer. Do this by clicking on the
y

axis and selecting Position. What does the area under a velocity
vs
. time graph represent? Test your
answer to this question using the Motion Detector.
10.
What type of motion is occurring when the slope of a velocity
vs
. time graph is zero?
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11.
What type of motion is occurring when the slope of a velocity
vs
. time graph is not zero? Test your answer
using the Motion Detector.
EXTENSIONS
1.
Create a graph

matching challenge. Sketch a position
vs
. time graph using the prediction feature of Logger
Pro
: Choose Draw Prediction from the Analyze menu, and use the mouse to draw a new target graph.
Challenge another student in the class to match your
graph. Have the other student challenge you in the
same way.
2.
Create a velocity
vs
. time challenge in a similar manner.
3.
Create a position
vs.
time graph by walking in front of the Motion Detector. Store the graph by choosing
Store Latest Run from the Expe
riment menu. Have another student match your run.
4.
Create a velocity
vs.
time graph by walking in front of the Motion Detector. Store the graph by choosing
Store Latest Run from the Experiment menu. Have another student match your run.
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