# Student Exploration: Distance-Time Graphs

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1 Name: Date: Procedure: Student Exploration: Distance-Time Graphs 1. Launch Internet Explorer 2. Go to 3. Click on Login. 4. Enter the Username: orange1011 Password: black Search for Distance-Time Graphs 6. Click on the 4 th Gizmo on the list called Distance-Time Graphs. 7. Be patient for it to load. Vocabulary: speed, y-intercept Prior Knowledge Questions (Do these BEFORE using the Gizmo.) Max ran 50 meters in 10 seconds. Molly ran 30 meters in 5 seconds. 1. Who ran farther, Max or Molly? 2. Who ran faster? Explain: Gizmo Warm-up The Distance-Time Graphs Gizmo TM shows a graph and a runner on a track. You can control the motion of the runner by manipulating the graph (drag the red dots). Check that Number of points is 2, and that under Runner 1 both Show graph and Show animation are turned on. The graph should look like the one shown to the right one point at (0, 0) and the other point at (4, 40). 1. Click the green Start button on the stopwatch. What happens?

2 2. Click the red Reset button on the stopwatch. The vertical green probe on the graph allows you to see a snapshot of the runner at any point in time. Drag it back and forth. As you do, watch the runner and the stopwatch. A. What was the position of the runner at 1 second? B. What are the coordinates of the point on the graph that tells you this? C. When was the runner on the 30-meter line? D. What are the coordinates of the point on the graph that tells you this? Activity A: Runner position Get the Gizmo ready: Click the red Reset button on the stopwatch. Be sure the Number of Points is 2. In the Gizmo, run the race many times with a variety of different graphs. (The red points on the graph can be dragged vertically.) Pay attention to what the graph tells you about the runner. 1. If a distance-time graph contains the point (4, 15), what does that tell you about the runner? (Be specific, and answer in a complete sentence.) 2. Look at the graph to the right. Notice where the green probe is. If you could see the runner and the stopwatch at this moment, what would you see? 3. Look at the image below, from the Gizmo. What must be true about this runner s graph?

3 4. The point on the graph that lies on the y-axis (vertical axis) is called the y-intercept. What does the y-intercept tell you about the runner? 5. In the Gizmo, set the Number of Points to 3. Then create a graph of a runner who starts at the 20-meter line, runs to the 40-meter line, and finishes at the 30-meter line. A. Sketch your graph to the right. B. What is the y-intercept of your graph? Activity B: Runner direction and speed Get the Gizmo ready: Click the red Reset button on the stopwatch. Run the Gizmo several times with different types of graphs. (Remember, the red points on the graph can be dragged vertically.) Pay attention to the speed and direction of the runner. 1. Create a graph of a runner that is running forward (from left to right) in the Gizmo. Sketch your graph to the right. If the runner is moving from left to right in the Gizmo, how does the graph always look? 2. Click the red Reset button. Create a graph of a runner that is running from right to left. Sketch it to the right. How does the graph always look if the runner is moving from right to left in the Gizmo?

4 3. Change the Number of Points to 5. Create a graph of a runner that runs left-to-right for one second, rests for two seconds, and then continues running in the same direction. Sketch the graph to the right. How does a graph show a runner at rest? 4. In general, how does a distance-time graph show you which direction the runner is moving? 5. With Number of Points set to 3, create the graph shown at right. Your graph should include (0, 0), (2, 10), and (4, 40). A. Where does the runner start? B. Where will he be after 2 seconds? C. Where will he be after 4 seconds? D. In which time interval do you think the runner will be moving most quickly? (Circle your answer below.) 0 to 2 seconds 2 to 4 seconds 6. Click the Start button and watch the animation. What about the runner changed after 2 seconds of running? 7. Speed is a measure of how fast something is moving. To calculate speed, divide the distance by the time. In the Gizmo, the units of speed are meters per second (m/s). A. In the first 2 seconds, how far did the runner go? B. In this time interval, how far did the runner go each second? C. In this time interval, what was the runner s speed?

5 8. Now look at the last two seconds represented on the graph. A. In the last 2 seconds, how far did the runner go? B. In this time interval, how far did the runner go each second? C. In this time interval, what was the runner s speed? 9. Click the Reset button. Experiment with a variety of graphs, focusing on the speed of the runner. In general, how can you estimate the speed of the runner by looking at a graph?

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