(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)

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To solve these questions, we can use the formula for speed, which is distance divided by time.

(a) To find Usain Bolt's speed, we need to know the distance he ran in the last 100 meters of the 150-meter race and the time it took him. Since the question states that he ran the last 100 meters in 8.70 seconds, we can use this information to find his speed.

Speed = Distance / Time
Speed = 100 meters / 8.70 seconds

To calculate the speed, divide the distance (100 meters) by the time (8.70 seconds). The answer will give you the speed at which Usain Bolt ran the last 100 meters.

(b) In this part, we need to find the duration of the acceleration period at the beginning of the race, assuming that Bolt accelerates at a constant rate up to his maximum velocity. Given that his maximum velocity is the speed calculated in part (a), we will use this information to solve the problem.

To find the duration of the acceleration period, first, we need to determine the total time of the race. Since the world record for the 100-meter dash is 9.58 seconds, we can subtract the time it took him to run the last 100 meters from the total time to find the duration of the acceleration period.

Acceleration Period Duration = Total Time - Time for Last 100 meters
Acceleration Period Duration = 9.58 seconds - 8.70 seconds

Subtract the time it took to run the last 100 meters (8.70 seconds) from the total time (9.58 seconds) to find the duration of the acceleration period.

(c) Finally, to determine the initial average acceleration in part (b), we can use the formula for average acceleration, which is the change in velocity divided by time.

Average acceleration = Change in velocity / Time

Since we are assuming a constant acceleration until reaching maximum velocity, the change in velocity is equal to the maximum velocity. We can use the formula for acceleration to solve this.

Average acceleration = Maximum velocity / Acceleration Period Duration

Divide the maximum velocity (speed calculated in part a) by the duration of the acceleration period (calculated in part b) to find the initial average acceleration.