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Author: Jack Bauer
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Student Exploration: Distance-Time and Velocity-Time Graphs

[NOTE TO TEACHERS AND STUDENTS: This lesson was designed as a follow-up to the Distance-Time Graphs Gizmo™. We recommend you complete that activity before this one.]

Vocabulary: displacement, distance traveled, slope, speed, velocity

Prior Knowledge Questions (Do these BEFORE using the Gizmo.)

Dora runs one lap around the track, finishing where she started. Clark runs a 100-meter dash along the straight side of the track.

Which runner traveled a greater distance? Which runner had a greater change in position, start to finish? Gizmo Warm-upThe Distance-Time Graphs Gizmo shows a dynamic graph of the position of a runner over time. The Distance-Time and Velocity-Time Graphs Gizmo includes that same graph and adds two new ones: a velocity vs. time graph and a distance traveled vs. time graph. The graph shown below (and in the Gizmo) shows a runner’s position (or distance from the starting line) over time. This is most commonly called a position-time graph.

Check that the Number of Points is 2. Turn on Show graph and Show animation for both Runner 1 and Runner 2. Drag the points to create the graph shown to the right.Runner 1’s line (the red one) should have endpoints at (0, 0) and (4, 40).Runner 2’s line (the blue one) should have endpoints at (0, 40) and (4, 20). Click the green Start button on the stopwatch. Watch the two runners carefully. In what two ways are the runners’ motions different?.Activity A:

Velocity-time graphs

Click the red Reset button on the stopwatch.
Change the Number of Points to 5.
Turn off Show graph and Show animationfor Runner 2.

Speed is a measure of how fast an object moves, regardless of direction. Speed can never be negative. Velocity describes both speed and direction, and can be positive or negative. In the Gizmo, make a position-time graph for Runner 1 with the following features:There is at least one major change in speed.There is at least one major change in direction. Click the green Start button and watch the runner run. Adjust your graph if needed to meet the requirements. Sketch your graph to the right. Where was the runner each second? Based on your graph, fill in all except the final column in the table below. (Leave the velocity column blank for now.) Label any numbers with units.

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