HPP A3v1
Modeling Human Walking:
Position and Velocity Graphs
In this activity we will investigate the relationship between position-time graphs and velocitytime graphs for a walking person.
Materials
DataStudio software
motion detector
number line on floor in meters (optional)
Exploration
You have looked at position and velocity-time graphs separately. Now you will see how they
are related.
GE 1. Predicting Velocity Graphs from Position Graphs
1. Suppose you are looking at a graph of position versus time for a person
walking in a straight line. Would this graph allow you to make predictions for
the shape of the velocity-time graph? Explain.
2. Download the DataStudio file dist_vel.ds, or set up DataStudio to show
both position-time and velocity-time graphs.
3. Carefully study the position graph shown below and predict the velocitytime graph that would result from the motion. Sketch your prediction of the
corresponding velocity-time graph on the velocity axes. Be as quantitative as
possible!
Activity Guide
© 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
HPP A3v1
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4. Make the graphs. After each person has sketched a prediction, Start, and
do your group's best to make a position graph like the one shown. Walk as
smoothly as possible.
When you have made a good duplicate of the position graph, paste the
postion and velocity-time graphs in the table below.
Paste the position-tim graph here….
Paste the velocity-time graph here….
5. How would the position graph be different if you moved faster? Slower?
6. How would the velocity graph be different if you moved faster? Slower?
Invention
GE 2.
1. Make a general statement that describes how a velocity-time graph for a
person walking in a straight line is related to the position-time graph of the
person.
2. Discuss your answer with the instructor. Note any changes you want to
make in the statement here.
GE 3. Estimating and Calculating Velocity
Activity Guide
© 2010 The Humanized Physics Project
HPP A3v1
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In this activity, you will estimate a statistical average velocity from the
velocity graph in Activity 1. Then, we will introduce a new physics concept
also called average velocity, which is different from a simple statistical
average or mean. We will calculate this “physics” average velocity using
your position graph.
1. Estimate your average velocity from your velocity graph in Activity 1.
You are to estimate an average value for velocity while you were walking
steadily in Activity 1. Select Examine in the Analysis Menu, then drag the
mouse over the graph and read a number of values (at least five) from the
velocity graph, and use them to calculate the average (mean) velocity. Make
sure you indicate the velocity units in the proper column heading. Also
estimate the uncertainty in the mean.
Velocity values read from graph:
Velocity (
Definition
)
Statistical Average value of the velocity:
(
)
Statistical uncertainty in the mean:
(
)
The physics average velocity during a particular time interval is the change of
position divided by the change in time. By definition, this is also the
(average) slope of the position-time graph for that time period.
As you have observed, the faster you move, the more inclined is your
position-time graph. The slope of a position-time graph is a quantitative
measure of this incline, and therefore it tells you the velocity of the object.
2. Calculate your physics average velocity from your position graph in
Activity 1. Use the Smart Tool to read the position and time coordinates for
two typical points while you were moving. For a more accurate answer, use
two points as far apart as possible but still typical of the motion, and within
the time interval over which you took velocity readings in (1). Remember to
include units in the parentheses!
Point 1
Position _______ ( )
Time ________ (
)
Point 2
Position _______ ( )
Time ________ (
)
Change in position:
( )
Change in time: (
Activity Guide
© 2010 The Humanized Physics Project
)
HPP A3v1
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Physics Average velocity :_______(
)
Calculate the change in position between points 1 and 2. Also calculate the
corresponding change in time (time interval). Divide the change in position
by the change in time to calculate the (physics) average velocity. Show your
calculations in the table above.
3. Is the average velocity positive or negative?
4. Does the (physics) average velocity you just calculated from the position
graph agree with the (statistical) average velocity you estimated from the
velocity graph? Do you expect them to agree? How would you account for
any differences?
Application
GE 4.
1. The figure below shows the position-time graph of a person walking in a
straight line. Sketch the corresponding velocity-time graph.
3.50
3.00
X [m]
2.50
2.00
1.50
1.00
0.50
0.00
0.00
0.50
1.00
1.50
2.00
2.50
2.00
2.50
3.00
t [s]
3
V [m/s]
2
1
0
-1
-2
-3
0.00
0.50
1.00
1.50
3.00
t [s]
2. What is the (physics) average velocity between 0.50 [s] and 1.0 [s] for the
person whose motion is shown in the graph above?
Activity Guide
© 2010 The Humanized Physics Project
HPP A3v1
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Application
GE 5. Predicting Position Graphs from Velocity Graphs
Predict a position(position)-time graph from a velocity-time graph. Carefully
study the velocity graph below. Using a dotted line, sketch your prediction of
the corresponding position graph on the bottom set of axes. (Assume that you
started at the 1-meter mark.)
2. Make the graphs. After you have sketched a prediction do your group's
best to duplicate the top (velocity-time) graph by walking. (Make sure the
Time axis is set 0 to 10 sec before you start. Ask your instructor how to do
this!)
When you have made a good duplicate of the velocity-time graph, paste your
graph here….
3. How can you tell from a velocity-time graph that the moving object has
changed direction?
Activity Guide
© 2010 The Humanized Physics Project
HPP A3v1
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4. What is the velocity at the moment the direction changes?
5. Is there something about the velocity-time graph above that is physically
impossible?
6. How can you tell from a position-time graph that your motion is steady
(motion at a constant velocity)?
7. How can you tell from a velocity-time graph that your motion is steady?
Activity Guide
© 2010 The Humanized Physics Project