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Distance-Time Graphs Answer Key
Vocabulary: speed, y-intercept
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
[Note: The purpose of these questions is to activate prior knowledge and get students thinking.
Students are not expected to know the answers to the Prior Knowledge Questions.]
Max ran 100 feet in 10 seconds. Molly ran 60 feet in 5 seconds.
1. Who ran farther, Max or Molly? Max ran farther.
2. Who ran faster? Molly
Explain: Molly ran 12 feet each second. Max ran 10 feet each second.
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 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? The runner runs from left to right for 4
seconds, stopping at the 40-yard line.
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? 10 yards
B. What are the coordinates of the point on the graph that tells you this? (1, 10)
C. When was the runner on the 30-yard line? At 3 seconds
D. What are the coordinates of the point on the graph that tells you this? (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.
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.)
This tells you that after 4 seconds of running, the runner was 15 yards from the starting line.
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 would be on the 20 yard line, facing left. The
stopwatch would read approximately 1.5 seconds (or 1:50).
3. Look at the image below, from the Gizmo. What must be true about this runner’s graph?
The graph of the runner must include the point (3.50, 25). [Students may also respond that
the graph has a positive, or “uphill,” slope at that point. This is because the runner is facing
forward in the image, so he must be running from left-to-right.]
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?
The y-intercept indicates the starting position of 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-yard line, runs to the
40-yard line, and finishes at the 30-yard line.
A. Sketch your graph to the right.
B. What is the y-intercept of your graph? (0, 20) or 20 yds
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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.
[Note: In each graph, there are several possible correct answers. Examples are given.]
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?
The graph will have a positive slope. (The line will go from
lower left to upper right.)
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?
The graph will have a negative slope. (The line will go from
upper left to lower right.)
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?
The line will be horizontal when the runner is at rest.
4. In general, how does a distance-time graph show you which direction the runner is moving?
The runner’s direction is given by the slope of the graph. A positive slope ( / ) indicates the
runner is moving forward, or from left to right. A negative slope ( \ ) indicates the runner is
moving backward, or from right to left.
(Activity B continued on next page)
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