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Student Exploration Distance Time Graphs

Explore distance-time graphs and runner motion with interactive Gizmo. Manipulate points to see how position changes over time, understand speed, and compare runners’ performance. Perfect for learning basic physics concepts visually and actively.

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    Student Exploration: Distance-Time Graphs Introduction: Calculating Speed Read the scenario below to answer the questions. Max ran 50 meters in 1 0 seconds. Molly ran 30 meters i n 5 seconds. 1. Wh o ran farther , Max or Molly? max 2. V/ho ran faster? Explain, including their speed. moly max- 50/10=5 m/s molly- 30/5=6 m/s Gizmo Warm-up The Distance-Time Graphs Gizmo 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 o f 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 (green) button on the stopwatch. Observe what happens. Click the red Reset (red) 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. 2. What was the position of the runner at 1 second? 10 meters What are the coordinates of the point on the graph that tells you this? (x : y) ( H O ) When was the runner on the 30 -meter line? 3 seconds What are the coordinates of the point on the graph that tells you this? (x : y) (3,30)

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    Activity A: Runner position Get the Gizmo ready: • Click the red Reset button on the stopwatch. • Be sure the Number of points is 2. Q 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.) it shows that at 4 seconds they ran 15 meters 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? the runner ran around 20 meters in 1.5 seconds 3. The point on the graph that lies on the y-axis (vertical axis) is called the y-intercept. In the graph above, the y-intercept is just above 20 on the y-axis. What does the y-intercept tell you about the runner? the y intercept tells you how much the runner has ran sofar 4. 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. Post a small screenshot of the graph below.

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    - i--------------- n Runner 1 y j Show graph / j s h c M animalKin R u n n e r 2 New / ] Show graph y j Show animalwn Number nt points

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    Activity B: Runner direction and speed Get foe Gizmo ready; • Click the red Reset button on the stopwatch. r t 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. Post a small screenshot of the graph below. r wssj Number of points I DfctnfK f Fnom s 1 4 rune (*+ccr*ls) R u n n e r 1 / S h o w graph / Shew arrnnanon Runner 2 New Show animation _ ] Show graph If the runner is moving from left to right in the Gizmo, hotv does the graph always look? the graph would always be slanting up towards the top right comer 2. Click the red Reset button. Create a graph of a runner that is running from right to left. Post a small screenshot of the staph below.

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