Student Exploration: Distance-Time and Velocity-Time Graphs
[NOTE TO TEACHERS AND STUDENTS: This lesson was designed as a follow-up to the
Distance-Time Graphs Gizmo™. We recommend you complete that activity before this one.]
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
Dora runs one lap around the track, finishing where she started. Clark
runs a 100-yard dash along the straight side of the track.
1. Which runner traveled a greater distance? ____Dora________
2. Which runner had a greater change in position, start to finish?
___Clark______________________________________
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? ___Runner 1 is running faster than runner 2 in an
opposite direction.__
This study source was downloaded by 100000847426977 from CourseHero.com on 06-03-2022 04:42:32 GMT -05:00
, Get the Gizmo ready:
Activity A: Click the red Reset button on the stopwatch.
Velocity-time Change the Number of Points to 5.
graphs Turn off Show graph and Show animation for
Runner 2.
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.
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.
Position at end Distance moved Velocity this
To the left or
Time of time interval this time time interval
right?
(yds) interval (yds) (y/s)
0 – 1 sec 16 yds 16 yds right 16 yds/s
1 – 2 sec 30 yds 14 yds right 14 yds/s
2 – 3 sec 38 yds 8 yds left 8 yds/s
3 – 4 sec 30 yds 8 yds left 8 yds/s
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 (y/s).
When this runner is running to the left (negative velocity), what does his position-time graph
look like?
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