(a) In 2009, Usain Bolt ran the last 100 meters of the 150-meter race in 8.70 seconds. What is Usain

Bolt’s speed?
(b) The world record for the 100-meter dash is 9.58 seconds (Bolt, 2009). Use the speed from part (a)
as his maximum velocity. Assume a sprinter accelerates at a constant rate up to their maximum
velocity, which is maintained for the remainder of the race, no matter how long it is. What is the
duration of the acceleration period at the beginning of the race?
(c) Determine the initial average acceleration in part (b).
(d) The record for the 200-meter dash is 19.19 seconds (Bolt, 2009), the 400-meter run is 43.18 seconds
(Johnson, 1999), the 800-meter run is 101.01 seconds (Rudisha, 2010), and for the 1500-meter run
it is 206.00 seconds (Guerrouj, 1998). Are these times consistent with the assumptions made?

9.58

9.58 sec.

(a) To calculate Usain Bolt's speed, we need to divide the distance he ran by the time it took him.

Given:
Distance = 100 meters (last 100 meters of the 150-meter race)
Time = 8.70 seconds

Speed = Distance / Time
Speed = 100 meters / 8.70 seconds
Speed = 11.49 meters per second

So, Usain Bolt's speed in the last 100 meters of the 150-meter race was 11.49 meters per second.

(b) To find the duration of the acceleration period at the beginning of the race, we need to consider the maximum velocity and the total time it took for the race.

Given:
Maximum Velocity = 11.49 meters per second (from part a)
Total Time = 9.58 seconds (world record for the 100-meter dash)

We can assume that the acceleration period is the time it takes to reach the maximum velocity. The remaining time is spent at the maximum velocity.

Acceleration Period = Total Time - Maximum Velocity Time
Acceleration Period = 9.58 seconds - 8.70 seconds
Acceleration Period = 0.88 seconds

So, the duration of the acceleration period at the beginning of the race is 0.88 seconds.

(c) To determine the initial average acceleration in part (b), we need to consider the change in velocity and the duration of the acceleration period.

Given:
Change in Velocity = Maximum Velocity - Initial Velocity
Change in Velocity = 11.49 meters per second - 0 meters per second (initial velocity)
Change in Velocity = 11.49 meters per second

Average Acceleration = Change in Velocity / Acceleration Period
Average Acceleration = 11.49 meters per second / 0.88 seconds
Average Acceleration = 13.06 meters per second squared

So, the initial average acceleration in part (b) is 13.06 meters per second squared.

(d) To determine if the given times for the 200-meter, 400-meter, 800-meter, and 1500-meter runs are consistent with the assumptions made, we need to compare the times with the expectations based on Usain Bolt's maximum velocity.

Given:
Maximum Velocity = 11.49 meters per second (from part a)

Let's calculate the expected times for the other distances using the maximum velocity:

Expected Time = Distance / Maximum Velocity

For the 200-meter dash:
Expected Time = 200 meters / 11.49 meters per second
Expected Time = 17.4 seconds

For the 400-meter run:
Expected Time = 400 meters / 11.49 meters per second
Expected Time = 34.8 seconds

For the 800-meter run:
Expected Time = 800 meters / 11.49 meters per second
Expected Time = 69.6 seconds

For the 1500-meter run:
Expected Time = 1500 meters / 11.49 meters per second
Expected Time = 130.6 seconds

Comparing the expected times with the given times:

200-meter dash (19.19 seconds) - The given time is greater than the expected time, suggesting that the assumption of maintaining the maximum velocity is not consistent.

400-meter run (43.18 seconds) - The given time is greater than the expected time, suggesting that the assumption of maintaining the maximum velocity is not consistent.

800-meter run (101.01 seconds) - The given time is greater than the expected time, suggesting that the assumption of maintaining the maximum velocity is not consistent.

1500-meter run (206.00 seconds) - The given time is greater than the expected time, suggesting that the assumption of maintaining the maximum velocity is not consistent.

Therefore, the given times for the 200-meter, 400-meter, 800-meter, and 1500-meter runs are not consistent with the assumptions made.