HPP A4
Modeling Human Walking:
Velocity and Acceleration Graphs
We saw in a previous activity that position-time graphs and velocity-time graphs were related to
each other. By knowing one you can figure out what the other looks like. In this activity we will
look at the relationship between velocity-time and acceleration-time graphs.
Exploration
GE 1.
1. Review your data from walking at constant velocity. Sketch your positiontime and velocity-time graphs for this situation.
x [m]
t [s]
v [m]
t [s]
2. Now, imagine that you are at the top of snow covered hill with a sled. You
place the sled on the snow, hop on it, and push yourself off so that you are
going down the hill. Describe, in words, what you think your motion will look
like.
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
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3. Assume that you have a good motion detector that can sense you on the sled
all the way down the hill. Draw how you think your position-time graph and
velocity-time graph will look for this trip.
x [m]
t [s]
v [m]
t [s]
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Go to the work area with a human-sized cart and incline plane.
Set the incline at height 1.
Download the DataStudio file dist_vel.ds at the computer in this work area.
Start up DataStudio and make sure you can get position-time and velocity-time data.
Pick a volunteer to sit on the cart at the top of the incline.
Obtain data for the motion of the person rolling down the incline.
Save your data for a later part of the investigation. (Select Save Activity as… on the File
Menu, name your file SPEEDUP.ds and place it in your group file exchange.)
Label the graphs on your display "Speeding Up" using the text button at the top of the graph
in DataStudio.
GE 2.
1. How does your position graph differ from the case for steady (constant
velocity) motion studied earlier?
Activity Guide
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2. What about the velocity graph shows that the motion was away from the
detector?
3. What about your velocity graph shows the cart and person were speeding
up? How is the graph different from the case of constant velocity?
4. Display velocity and acceleration. Drag the acceleration icon (in the
Data Summary window on the left of the screen in DataStudio) down to the
graph icon directly below it (in the Displays window). You should now have
three graphs on your display.
During the time that the cart is speeding up, is the acceleration positive or
negative? How does speeding up while moving away from the detector result
in this sign of acceleration? Hint: Remember that acceleration is the rate of
change of velocity. Look at how the velocity is changing.
5. How does the velocity vary in time as the cart speeds up? Does it increase
at a steady rate or in some other way?
6. How does the acceleration vary in time as the cart speeds up? Is this what
you expect based on the velocity graph? Explain.
7. Suppose you increase the height of the incline and repeat the motion. How
would the acceleration change?
8. How would the velocity and acceleration graphs change from the motion
with height 1?
9. Repeat the experiment with the incline at twice its original height. Save
your activity file, data, for later use. Make sure both runs are visible on the
display. Paste your graphs for position, velocity and acceleration below.
10. Did the shapes of the velocity-time and acceleration-time graphs agree
with your predictions?
Activity Guide
 2010 The Humanized Physics Project
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11. How is the magnitude (size) of the acceleration represented on a velocitytime graph?
12. How is the magnitude of the acceleration represented on an accelerationtime graph?
Now we will investigate slowing down.
Take the cart off the incline and set up an area where the cart can travel horizontally away from
the detector.
Place a towel between cart and floor so that there is some drag.
Choose a volunteer to sit on the cart.
Practice giving the cart and rider a push, letting go, and allowing the cart to come to rest.
GE 3.
1. If you give a cart with drag a push away from the detector and let it slow
down, will the acceleration be positive, negative, or zero, after the cart is
released?
2. Predict the shape of the velocity-time and acceleration-time graphs for this
case.
Activity Guide
 2010 The Humanized Physics Project
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3. Load the dist_vel.ds file into DataStudio, and add the acceleration graph.
Take data for the motion described above. Save the file (rename it
SLOWDOWN.ds). Paste the velocity and acceleration graphs below. Label
the graphs with
"A" at the spot where you started pushing.
"B" at the spot where you stopped pusing.
"C" at the spot where the cart stopped coasting.
4. Did the shapes of your velocity and acceleration graphs agree with your
predictions? How is the sign of the accleration represented on a velocity-time
graph?
5. How is the sign of the acceleration represented on an acceleration-time
graphs?
6. Try to develop a general rule for predicting the sign of the acceleration from
the velocity graph.
7. Does your rule correctly predict what you observed for the cart moving
away from the detector, speeding up? How about for the case of moving away
from the cart, slowing down?
8. Use your rule to predict the sign of the acceleration for the following case:
the cart moves towards the detector slowing down.
9. Sketch predicted shapes of the velocity-time and acceleration-time graphs.
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10. Conduct the actual experiment with the cart and rider. Sketch (or paste)
the velocity and acceleration graphs based on your data.
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 2010 The Humanized Physics Project
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11. What aspect of the velocity graph shows that the motion was towards the
detector?
12. What aspect of the velocity graph shows that the person was slowing
down.?
13. How was your prediction for the acceleration?
14. If you need to revise your rule for predicting the sign of the acceleration
from the velocity-time graph, do so here.
Invention
We have found from previous investigations that the instantaneous velocity of a person walking
can be determined from the slope of position-time graph. If the slope of the x-t is constant, then
instanteous velocity is constant (horizontal line on the v-t graph). In this investigation we see
that acceleration tells us something about the slope of the velocity-time graph.
Application
GE 4.
Suppose the person-cart is placed on an incline that points down to the
detector.. You can expect that the cart go towards the detector, but speed up.
1. Sketch predictions for the velocity and acceleration graphs.
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2. What do you predict the sign of the acceleration will be?
We will not try this experiment with the human-cart system, as it is difficult to do safely.
Take the drag off the cart so that it can roll freely on the floor. Suppose a person climbs on the
cart and receives a push so that the cart rolls freely at approximately constant velociy away from
the detector.
GE 5.
1. What is your prediction for the acceleration of the person-cart in this
situation?
2. Try the experiment. Describe the results.
Activity Guide
 2010 The Humanized Physics Project