Sprinting Data from the 2008 Beijing Olympics

The following graph shows real data for Usain Bolt – one of the fastest persons ever to live.  The data are plotted along with a best-fit curve.  Except for the first question use the best-fit curve to answer the questions.

Time (s)  Distance (m)

  0.000         0.00

  0.165         0.00

  1.865         10.0

  2.865         20.0

  3.765         30.0

  4.635         40.0

  5.485         50.0

  6.325         60.0

  7.145         70.0

  7.975         80.0

  8.825         90.0

  9.685       100.0

1. Use the data table to determine Bolt’s average speed for the 100 m dash.

2. Inspect the graph closely and note that there is a curved section followed by a linear section.  Use a ruler held against the linear section to determine the approximate point in time where the graph changes from a curve to a line.

3. What is the significance of the curved section?  In other words how was Bolt moving such that the graph curves upward?

4. What is the significance of the linear section?  In other words how was Bolt moving such that the graph is linear?

5. During what interval of time was Bolt’s speed essentially constant and how is this apparent?

6. Determine the maximum speed attained by Bolt.  This will be the slope of the graph where ever it is maximized.  (Do not use the data table.)

7. Determine the speed of Bolt at 2.00 seconds into the race.

Hypothetical Motion of an Automobile

This graph shows plausible and realistic information for a typical car in motion along a straight road.  Note that the position of the car is related to a stoplight that the car encounters.

1. Determine the car’s initial position, final position, and displacement.

2. Based on the change in position, which direction was the car moving on the road?

3. Determine the car’s average velocity and its average speed.

4. Use a ruler to determine which parts of the graph are linear and which parts are not.  Now describe the car’s motion for each distinct interval by using a statement of the form: 
“From ?   to ? seconds the car’s speed was increasing/decreasing/constant?.”

5. Determine the velocity of the car at 5.00 seconds.

6. Determine the velocity of the car at 12.0 seconds.

7. Determine the speed of the car at 12.0 seconds.

8. Determine the speed of the car at 25.0 seconds.

9. Determine the speed of the car at 28.0 seconds.

Answers for Usain Bolt:

1. 10.33 m/s (or 10.50 m/s excluding reaction time)

2. t = 4.0 s

3. The curved section indicates that Bolt was accelerating and his speed was increasing.

4. The linear section indicates that Bolt reached his top speed and did not accelerate for the last six seconds of the race.

5. Because slope equals speed the linear pattern of the data shows the speed to be fairly constant in this interval of time:  4.0 s < t < 9.9 s.

6. 12.1 m/s (that’s 27.1 mph!)

7. At t = 2.00 s, v = 9.1 m/s

Answers for Car Approaching Stoplight:

1. s_i = 485 m, 90° from stoplight (or 485 m, north of stoplight)
s_f = 10 m, 90° from stoplight (or 10 m, north of stoplight)
d = 475 m, 270°  (or 475 m, south)

2. The car is located north of the stoplight but traveling south on the road toward the stoplight.

3. v_avg = 15.8 m/s, 270°; v_avg = 15.8 m/s

4. From 0 to 10 s the car’s speed was increasing.
From 10 to 22 s the car’s speed was constant.
From 22 to 26 s the car’s speed was decreasing.
From 26 to 30 s the car’s speed was zero.

5. 12.5 m/s, 270°

6. 25.0 m/s, 270°

7. 25.0 m/s

8. 6.3 m/s

9. 0 m/s