Modeling Human Walking: Position and Velocity Graphs

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1 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! Supported in part by NSF-CCLI Program under grants DUE # and DUE #

2 HPP A3v 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 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

3 HPP A3v1 3 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: ( ) ( )

4 HPP A3v1 4 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 The figure below shows the position-time graph of a person walking in a straight line. Sketch the corresponding velocity-time graph X [m] t [s] 3 2 V [m/s] 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?

5 HPP A3v1 5 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?

6 HPP A3v 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?

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