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. 1. Which runner traveled a greater distance? 2. Which runner had a greater change in position, start to finish? Gizmo Warm-up The 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. 1. 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). 2. Click the green Start button on the stopwatch. Watch the two runners carefully. In what two ways are the runners’ motions different? Dora Clark One’s displacement is higher and the others distance is higher. But the one that has the higher displacement had less distance walked. Student Exploration: Distance-Time Velocity and Velocity-Time Graphs Page 2 of 8 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. 1. 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. Click on the graph, then click Edit. Use the sketch tool to draw, then click Save & Close. 2. 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. Time Position at end of time interval (m) Distance moved this time interval (m) To the left or right? Velocity this time interval (m/s) 0 - 1 sec 10 10 right 10 1 -2 sec 40 30 right 30 2 - 3 sec 30 10 left -10 3 - 4 sec 20 10 left -10 Student Exploration: Distance-Time Velocity and Velocity-Time Graphs Page 3 of 8 3. To calculate the velocity for each time interval, first calculate the speed of the runner in that interval (speed = distance ÷ time). If the direction is left to right, velocity is positive. If the direction is right to left, velocity is negative. Fill in the velocity column of the table above. Use units (m/s). When this runner is running to the left (negative velocity), what does his position-time graph look like? 4. Slope is the steepness of a graph. To find the slope of a line, divide the change in y-value (rise) by the change in x-value (run). Like velocity, slope can be positive, zero, or negative. Fill in the slope of each segment of your position-time graph, along with the runner’s velocity during each time interval, in the table below. Time interval Slope Velocity (m/s) 0 sec - 1 sec 10 10 1 sec - 2 sec 30 30 2 sec - 3 sec -10 -10 3 sec - 4 sec -10 -10 5. Examine your velocities and the position-time graph you made. How is the slope of a position-time graph related to the velocity of the runner? 6. On the left side of the Gizmo, select the VELOCITY-TIME GRAPH tab. Use the green probes to compare the velocity-time graph to the position-time graph. A. How does a velocity-time graph show that a runner is moving fast? It has a negative slope. They are the same. A horizontal line would have a greater y coordinate