Investigation 3B: Motion graphs

Essential questionsHow 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 velocity-time graphs below.
Part 1: Matching the motion of a Smart Cart

Push the Smart Cart on the track
  1. Set up your equipment like the picture.
  2. Open the experiment file 03B_MotionGraphs, and then power-on the Smart Cart and connect it wirelessly to the software.
  3. Do the following for each velocity-time graph on pages 1 through 4 of the experiment file.
    1. Sketch a prediction for the corresponding position-time graph. Label the prediction.
    2. Find the page in the experiment file with the corresponding velocity-time match graph. Hide any data so the position-time graph is blank and only the velocity-time match graph is shown.
    3. 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 velocity-time data matches the velocity-time match graph.
    4. Sketch the actual position-time graph in the same graph as your prediction.
  1. How does the position graph for a high positive velocity differ from a lower positive velocity?
  2. How does the velocity graph for a high positive velocity differ from a lower positive velocity?
  3. How does the position graph for a negative velocity differ from positive velocity?
  4. How does the velocity graph for a negative velocity differ from a positive velocity?
  5. Describe a situation for which the position versus time graph and the velocity versus time graph are both flat (zero slope) horizontal lines.
A position versus time graph with four different slopes labeled
  1. Go to page 5 in the experiment file and hide any data so the velocity-time graph is blank and only the position-time match graph is shown. Record data to match the position-time 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.
  2. Draw the resulting velocity-time graph. Label each section corresponding to the letters in the position-time graph above.
  3. Use the slope tool in your software to find the slope of the position-time 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 constant-velocity model for position vs. time

How to use the velocity, position, and time simulationThis 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, xi and v, so that the line hits both targets.
  1. [SIM] starts the simulation. [Stop] stops it without changing values. [Clear] resets all variables to zero. [Reset] resets all variables and sets new targets.
  2. 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.
  3. Use the print button to print out a copy of your solution and score.
  1. Describe the meaning of xi and v in this model for the motion of a cart.
  2. What velocity will move an object from +50 m to −50 m in 20 s? Show your work.
  3. 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 xi 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

How to use the advanced velocity, position, and time simulation
  1. The second interactive model contains four constant-speed segments.
  2. Your goal is to adjust the values of xi and v for all sections to hit the four targets.
  3. Enter values in the white boxes. The top score of 100 is achieved by hitting the center of each target.
  4. Simulate your model to see how it runs on the graphs of its motion.
  1. In this model for the motion of the ErgoBot, there are four values of xi. Where do the three values of xi in the gray boxes come from?
  2. Describe how this model could be generalized to recreate any motion in one dimension.
In this interactive simulation, you will adjust the initial position xi 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.

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