Name_______________________________
Date_________________
PRE-LAB: ACCELERATION AND VELOCITY
1. In Investigation 1, Activity 1, how do you expect that your
position-time graphs will differ from those where you were moving
with a constant velocity? How about your velocity-time graph?
2. In Investigation 1, Activity 2, what quantity are you using the
linear fit function to find?
3. In Investigation 2, Activity 1, explain how to use the fan to make
the cart slow down instead of speed up:
4. Draw your predictions for Speeding Up Towards the Motion
Detector (Investigation 2, Activity 3):
1
Lab Group Members:
Date:
Acceleration and Velocity
PURPOSE: Analyze the sign of acceleration for motion with changing velocity.
EQUIPMENT: Motion detector, USB cable, computer, Logger Pro software, cart, track,
fan attachment with 4 AA batteries.
INVESTIGATION 1 – MEASURING ACCELERATION
Activity 1 – Speeding up away
PROCEDURE:
Open Logger Pro Experiments folder to Additional Physics, RealTime Physics,
Mechanics, L02A1-1 (Speeding Up ).
Set up the cart, ramp and motion detector as indicated below. Make sure the ramp is level
and that the cart is at least 20 cm in front of the motion detector, and that the fan is
attached securely.
Conserve batteries and fight noise pollution by turning fan on only when collecting data.
Turn on the fan, release the cart and collect the data. The fan makes the cart move with a
reasonably constant acceleration. We can ignore slight variations. The cart should
move away from the motion detector and speed up. When you obtain a good data run
(relatively horizontal line acceleration), Store Latest Run (Experiment menu).
1. Examine the position-time graph. How is it different from a position graph for
constant velocity? To see the differences more clearly, move the cursor to the time axis,
where it will turn into a wavy line. Use that to compress the position graph. Before
moving to the next question, go to Edit and Undo your changes.
2. Examine the velocity-time graph. How is it different from a velocity graph for
constant velocity?
2
3. Examine the acceleration-time graph. What feature indicates that it is constant
acceleration?
4. How is direction of acceleration (different from direction of motion!) indicated on an
acceleration-time graph?
5. Explain why acceleration is positive for this motion:
Activity 2 – Statistics and Curve-Fit
Using statistics: You can use the statistics feature to find the mean acceleration from
the acceleration graph. Click on the acceleration graph to make it active. Select the
portion of the acceleration graph that you want to use and click on the “STAT” icon:
1. Mean acceleration: magnitude:________ m/s/s
sign___________
2 . Compare the acceleration and velocity graphs. Are the signs of acceleration and the
velocity the same, or different (circle the correct answer)?
Using linear-fit: You can use the linear-fit feature to find the equation of the best-fit
curve for the velocity graph. Select the portion of the velocity graph that you want to use
(same as the acceleration graph) and click on the linear fit icon (“R=”).
3. Δv/Δt (slope): magnitude:_______ units________
sign__________
4. State explicitly the relationship between the value of the acceleration graph and the
slope of the velocity graph for motion with constant acceleration:
5. Record the equation of the best-fit curve with the given values:___________________
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Using curve-fit: Use the curve-fit feature to find the equation of the best-fit curve for the
position graph. Select the portion of the position graph that you want to use (same as the
acceleration graph) and click on the curve-fit icon (f(x)=). The position graph for
constant acceleration is described by a quadratic equation. Click on the “try fit” button to
generate the curve-fit.
4. Record the equation of the best-fit curve with the given values:___________________
5. Can you recognize any of the coefficients (A,B,C) from the best-fit curve for of the
velocity graph? Which one (or ones)?
6. Print your graphs, with analysis boxes not blocking the actual data. Title the graph
“Speeding up Away”.
INVESTIGATION 2 – DIRECTION OF VELOCITY AND ACCELERATION
Activity 1 – Slowing down away
DO NOT CHANGE EXPERIMENT FILE. For this activity, the fan should be pushing
the cart towards the motion detector. Now if you push the cart away, it will slow down.
Turn the fan unit on and begin graphing. Give the cart a gentle push away from the
motion detector. The relevant part of the graph occurs from after you’ve stopped
pushing, (i.e. cart is moving on its own) until the cart stops. Identify this portion of your
data for analysis. When you get a good data run, print your graphs (no further data
analysis). Title should now be (you guessed it) Slowing Down Away.
Mark the start and end of the relevant portion of your data with a pencil, so I can
see that you know where it is.
1. Describe the position-time graph. Comparing it to Speeding Up Away, what feature
shows slowing down (compress graph to see better)?
2. What is the sign of the velocity values? _________ The sign of the slope _________?
3. The sign of the acceleration graph should be negative (Verify!). Why is the sign of
the acceleration opposite to that of the sign of the velocity graph values for this motion?
Choose the best hypothesis:
A. Slowing down always results in negative acceleration.
B. When an object slows down, velocity and acceleration have opposite signs.
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Activity 2 – Slowing down towards
1. Based on your answer to the above multiple-choice question, predict the sign of the
acceleration graph for this motion. This question is graded on logic, not correctness!
________________
2. Clear all data from the previous graph, including title, and repeat the above procedure
for slowing down towards the detector . The relevant part of the graph occurs from after
you’ve stopped pushing, (i.e. cart is moving on its own) until the cart stops. Identify this
portion of your data for analysis. When you get a good data run, print your graphs.
Mark the start and end of the relevant portion of your data with a pencil. Title your
graph Slowing down towards.
3. Describe the position-time graph. Comparing it to Slowing Down Away, what feature
shows motion towards the detector, (compress graph to see better)?
4. Explain why the sign of the velocity values are negative during the time the cart is
slowing down. Recall that for “Slowing Down Away” velocity values were positive.
3. What is the sign of acceleration? ______________
4. Why is the sign of the acceleration opposite to that of the sign of the velocity graph
values for this motion? Choose the best hypothesis:
A. Slowing down always results in negative acceleration.
B. When an object slows down, velocity and acceleration have opposite signs.
Did you change your hypothesis from the last time this question was asked?
5
Activity 3 – Speeding up towards
Get your prelab back with your prediction for this motion.
Clear all data from the previous graph and repeat the above procedure for the motion
described above. Don’t let the cart hit the motion detector!! When you get a good data
run, print your graphs, with the appropriate title.
1. How did the shapes of your velocity and acceleration graphs compare with your
predictions? If they were not the same, explain:
2. Fill in the table:
Type of Motion
sign of velocity
sign of acceleration
Speeding Up in Positive Direction
Slowing Down in Positive Direction
Slowing Down in Negative Direction
Speeding Up in Negative Direction
4. How do the signs of velocity and acceleration relate when
a) the object is speeding up
b) the object is slowing down
5. Which one or more of the graphed quantities always shows the direction of the
motion?
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INVESTIGATION 3 – REVERSING DIRECTION - THE TURNING POINT
In this activity you will look at what happens when the cart slows down away from the
motion detector, reverses direction and then speeds up towards the motion detector.
A. Prediction
1. Using your previous observations as a guide, draw a prediction of this situation on the
axes that follow.
REVERSING DIRECTION
2. For each part of the motion, indicate in the table below whether signs of velocity and
acceleration vectors are positive, negative or zero.
Moving away
The turning point
Moving toward
Velocity
Acceleration
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B. Experiment
Test your predictions. Clear all data from the previous graph and give the cart enough of
a push so it travels about one-half meter before it returns. Don’t let the cart hit the
motion detector!! When you get a good data run, (A, B, and C, below, must be visible),
print your graphs. Make an identifying title for your graph. The relevant part of the
graph occurs from after you’ve stopped pushing, (i.e. cart is moving on its own) until just
before you stop the cart on its return trip.
3. With pen or pencil, label the following points on both graphs:
A. where your hand left the cart
B. the turning point
C. where you stopped the cart
How did you determine where each of these points is? If any of these points is NOT on
your graph, state this explicitly?
4. Did the cart stop at its turning point (i.e. v = 0)? Does this agree with your prediction?
Did it spend any time at the turning point velocity before starting back toward the
detector? Explain:
5. According to the graph, what is the acceleration at the instant the cart reaches its
turning point? Does this agree with your prediction? Using the definition of acceleration
(∆v/∆t) explain how the acceleration can be non-zero when the velocity is zero at some
instant.
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INVESTIGATION 5 GRAPH ANALYSIS
After studying the acceleration and velocity graphs you made, answer the following
questions.
+
A
c
c 0
0
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l
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4
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10 T i m e
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1. An object moving along a line (the + distance axis) has the acceleration-time
graph above. How might the object move to create this graph
A. If it is moving away from the origin
___________________________________________________________
___________________________________________________________
B. If it is moving toward the origin
___________________________________________________________
___________________________________________________________
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2. Sketch on the axes below the velocity-time graphs that go with the above
acceleration-time graph (for cases A and B). Label your graphs.
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T i m e (s e c)
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3. How would an object move to create each of the three labeled parts of the
acceleration-time graph above?
a:____________________________________________________________
b:________________________________________________________________
c:________________________________________________________________
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4. Sketch below a velocity-time graph which might go with the above acceleration-time
graph.
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5. For each of the velocity-time graphs below, sketch the shape of the acceleration-time
graph that goes with it.
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6. A car moves along a line [the + distance (position) axis]. Fill in the table below with
the sign (+ or -) of the velocity and acceleration of the car for each of the motions
described.
Distance
(Position)
Car moves
away from
the origin
+
Car moves
toward the
origin
+
Velocity
Acceleration Acceleration
Slowing
Speeding
Up
Down
7. Which position-time graph below could be that for a cart that is steadily accelerating
away from the origin?
a)
b)
D
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c)
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Time
Time
Time
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8.
Describe how you would move
to produce the velocity time
graph on the right.
____________________________
____________________________
____________________________
9.
Sketch a distance-time graph
graph for this motion on the
axes on the right.
10. Sketch an acceleration-time
graph for this motion on the
axes on the right.
V+
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c 0
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s
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c
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Time
Time
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c 0
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11-13. A car can move in either direction along a line (the + distance axis). Sketch
velocity-time and acceleration-time graphs which correspond to each of the following
descriptions of the car's motion. Use the axes provided on the following page.
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11. The car starts from rest, and
moves away from the origin
increasing its speed at a
steady rate.
V
+
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c
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t y
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c 0
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12. The car is moving toward
the origin at a constant
velocity.
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t y
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c 0
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Time
Time
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13. The car starts from rest, and
moves toward the origin,
speeding up at a steady rate.
V
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c 0
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14. The following is a velocity-time graph for a car.
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What is the average acceleration of the car? Show your work below.
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
15. A ball is tossed in the air. It moves upward, reaches its highest point and falls back
downward. Sketch a velocity-time and an acceleration-time graph for the ball from
the moment it leaves the thrower's hand until the moment just before it reaches her
hand again. Consider the positive direction to be upward.
V +
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l
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c 0
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Time
A
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c 0
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Time
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16. Sketch the following graphs. Assume constant acceleration:
a. an object speeding
up in a positive
direction:
b. an object speeding
up in a negative
direction:
c. an object slowing
down in a positive
direction:
d. an object slowing
down in a negative
direction:
16