
Essential questions   How do we predict an object’s position at a later time?  

Graphs and equations are valuable methods for describing the motion of an object. Position versus time and velocity versus time graphs can describe where an object is located, how fast it is going, and which direction it is headed. In this activity you will adjust the motion of a Smart Cart to match the velocitytime graphs below.

Part 1: Matching the motion of a Smart Cart


 Set up your equipment like the picture.
 Open the experiment file 03B_MotionGraphs, and then poweron the Smart Cart and connect it wirelessly to the software.
 Do the following for each velocitytime graph on pages 1 through 4 of the experiment file.
 Sketch a prediction for the corresponding positiontime graph. Label the prediction.
 Find the page in the experiment file with the corresponding velocitytime match graph. Hide any data so the positiontime graph is blank and only the velocitytime match graph is shown.
 Place the cart on the track and record data as you push, pull, roll, or use your hand to move the cart so that its velocitytime data matches the velocitytime match graph.
 Sketch the actual positiontime graph in the same graph as your prediction.

 How does the position graph for a high positive velocity differ from a lower positive velocity?
 How does the velocity graph for a high positive velocity differ from a lower positive velocity?
 How does the position graph for a negative velocity differ from positive velocity?
 How does the velocity graph for a negative velocity differ from a positive velocity?
 Describe a situation for which the position versus time graph and the velocity versus time graph are both flat (zero slope) horizontal lines.

 Go to page 5 in the experiment file and hide any data so the velocitytime graph is blank and only the positiontime match graph is shown. Record data to match the positiontime graph, and then describe the motion of the cart during each section shown in the graph to the right. Use terms such as forward, backward, at rest, fast, and slow.
 Draw the resulting velocitytime graph. Label each section corresponding to the letters in the positiontime graph above.
 Use the slope tool in your software to find the slope of the positiontime graph in each section A, B, C, and D. Record the slopes. How does the slope of the position time graph compare to the velocity recorded during the same period?

Part 2: The constantvelocity model for position vs. time
This interactive, graphical model shows position and velocity versus time graphs for the motion of a cart. Red circles on the position versus time graph are “targets.” Your goal is to adjust the initial parameters, x_{i} and v, so that the line hits both targets.
 [SIM] starts the simulation. [Stop] stops it without changing values. [Clear] resets all variables to zero. [Reset] resets all variables and sets new targets.
 Enter values in the white boxes. Gray boxes are calculated and cannot be edited. The top score of 100 is achieved by crossing the center of each target circle.
 Use the print button to print out a copy of your solution and score.
 Describe the meaning of x_{i} and v in this model for the motion of a cart.
 What velocity will move an object from +50 m to −50 m in 20 s? Show your work.
 Find a solution yourself, then press [Clear] and have your partner find a solution. How well do your two solutions agree? Is one solution better than the other?

In this interactive simulation, you will adjust the initial position x_{i} and velocity v of a cart so that a position vs. time graph of its motion matches graphical targets.

Part 3: A more complex model
 The second interactive model contains four constantspeed segments.
 Your goal is to adjust the values of x_{i} and v for all sections to hit the four targets.
 Enter values in the white boxes. The top score of 100 is achieved by hitting the center of each target.
 Simulate your model to see how it runs on the graphs of its motion.
 In this model for the motion of the ErgoBot, there are four values of x_{i}. Where do the three values of x_{i} in the gray boxes come from?
 Describe how this model could be generalized to recreate any motion in one dimension.

In this interactive simulation, you will adjust the initial position x_{i} and four different velocities v—for each of four time periods—of the cart so that a position vs. time graph of its motion matches graphical targets.
