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. If we assume that Bolt accelerated for 3.00 s to reach his maximum speed, and maintained that speed for the rest of the race, calculate his maximum speed and his acceleration. (a) In your notebook, draw a sketch of the run. The 100 m-dash is made up of what two motions? Label the sketch with vectors for velocity and acceleration at the start and finish and at the end of each motion.

Answer 1

Answer:

$a = 4.07 m/s^2$

now his maximum speed is given as

$v = 3a = 12.21 m/s$

Explanation:

Total time for which Usain Bolt accelerated is given as

$t_1 = 3 s$

now the velocity after uniform acceleration is given as

$v_1 = 0 + 3a$

now remaining time for which he run for the finish line is given as

$t_2 = (9.69 - 3) = 6.69 s$

now the distance moved by him during uniform acceleration is given as

$d_1 = \frac{1}{2}a(3^2)$

$d_1 = 4.5 a$

another distance that he moved for uniform speed is given as

$d_2 = (3a)(6.69)$

$d_2 = 20.07 a$

now total distance moved by him is 100 m so we have

$20.07 a + 4.5 a = 100$

$a = 4.07 m/s^2$

now his maximum speed is given as

$v = 3a = 12.21 m/s$