(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)
(a) v = 100 m / 8.70 s
(b) constant acceleration (from zero) means that the average velocity during the acceleration phase is half of the final velocity
(v/2) t + v (9.58 - t) = 100 m
plug in v and solve for t
(c) average acceleration is v/t
(a) To calculate Usain Bolt's speed, we need to divide the distance he ran (100 meters) by the time it took him (8.70 seconds). Speed is defined as distance divided by time.
Speed = Distance/Time
So, Usain Bolt's speed is:
Speed = 100 meters / 8.70 seconds = 11.49 meters per second
Therefore, Bolt's speed is approximately 11.49 meters per second.
(b) In this part, we are given that Usain Bolt's maximum velocity is the speed calculated in part (a), which is 11.49 meters per second. We need to determine the duration of the acceleration period at the beginning of the race.
Since Bolt accelerates at a constant rate until reaching his maximum velocity, we can use the formula for acceleration:
Acceleration = Change in Velocity / Time
We know the change in velocity is the difference between the maximum velocity (11.49 m/s) and the initial velocity (0 m/s). Therefore:
Acceleration = (11.49 m/s - 0 m/s) / Time
We can rearrange the formula to solve for time:
Time = Change in Velocity / Acceleration
Plugging in the values, we get:
Time = (11.49 m/s - 0 m/s) / Acceleration
To find the duration of the acceleration period, we need to know the acceleration rate, which is not given in the question. Please provide the acceleration rate to continue with the calculation.
(c) To determine the initial average acceleration in part (b), we need to know the duration of the acceleration period and the change in velocity.
Using the formula:
Acceleration = Change in Velocity / Time
We know the change in velocity is the difference between Bolt's maximum velocity (11.49 m/s) and his initial velocity (0 m/s). We also need the duration of the acceleration period, which was not provided in the question.
Please provide the duration of the acceleration period to calculate the initial average acceleration.