Or

Author:
Jack Bauer

Student Exploration: Distance-Time Graphs

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.

Who ran farther, Max or Molly?

Who ran faster? ____ ________ Explain: Molly ran 6 meters per second while Max ran ________________________________________

Gizmo Warm-up

The Distance-Time Graphs GizmoTM 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).

Click the green Start button on the stopwatch.

What happens?.

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.

What was the position of the runner at 1 second? __________ ______________

What are the coordinates of the point on the graph that tells you this?

When was the runner on the 30-meter line? ______________________________

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.

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.)

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?

Look at the image below, from the Gizmo. What must be true about this runner’s graph?

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?

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.

Tutorial