Question

A world record was set for the men’s 100-m dash in the 2008 Olympic Games in Beijing by Usain Bolt of Jamaica. Bolt "coasted" across the finish line with a time of 9.69 s.

a. If we assume that Bolt accelerated at constant acceleration for 3.00 s to reach his maximum speed and maintained that speed for the rest of the race, calculate his maximum speed in meters per second.
b. Using the assumptions of part (a) calculate Bolt's acceleration in meters per second squared.
c. During the same Olympics, Bolt also set the world record in the 200-m dash with a time of 19.30 s. Using the same assumptions as for the 100-m dash, what was his maximum speed for this race in meters per second?

Answer 1

To calculate Usain Bolt's maximum speed in the 100-m dash, we need to find his acceleration first. Assuming constant acceleration, his maximum speed and acceleration can be calculated using the given time of 9.69 s. The same assumptions can be applied to find his maximum speed in the 200-m dash.

Step-by-step explanation:

To find Usain Bolt's maximum speed in meters per second, we need to calculate the acceleration first. According to the question, Bolt accelerated for 3 seconds to reach his maximum speed, and then maintained that speed for the rest of the race. Let's assume his acceleration is constant.

Using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can calculate the final velocity. Initially, Bolt's speed is 0 m/s because he is at rest. After accelerating for 3 seconds, his final velocity is given by v = 0 + (a * 3).

Let's assume Bolt reaches his maximum speed of v_1 m/s after 3 seconds. Therefore, v_1 = 3a.

Now, his speed remains constant for the rest of the race, so v_1 is equal to the maximum speed. Hence, Bolt's maximum speed is v_1 m/s.

To find Bolt's acceleration in meters per second squared, we can use the formula v = u + at again. Since Bolt's initial velocity is 0 m/s after accelerating for 3 seconds, his final velocity is v_1 m/s. Therefore, v_1 = 0 + a * 3. From this equation, we can solve for a. Thus, Bolt's acceleration is a m/s^2.

For part (b), we can apply the same approach. Bolt's maximum speed for the 200-m dash is given as v_2. Initially, his speed is 0 m/s, and after accelerating for 3 seconds, his final velocity is v_2. Using the formula v = u + at, we can calculate the final velocity. Thus, v_2 = 0 + (a * 3). Since v_2 represents Bolt's maximum speed, v_2 = 3a.

Hence, Bolt's maximum speed for the 200-m dash is v_2 m/s.