A certain sprinter has a top speed of 10.5 m/s. If the sprinter starts from rest and accelerates at a constant rate, he is able to reach his top speed in a distance of 12.0 m. He is then able to maintain his top speed for the remainder of a 100 m race. (a) What is his time for the 100 m race

Total time = 10.667 seconds

Explanation:

For the first 12m

V² = u² + 2as

10.5² = 0² + 2a (12)

110.25 = 24a

a = 4.59375 m/s²

V = u + at

10.5 = 0 + 4.59375t

t = 10.5/4.59375

t = 2.286 seconds

For the remaining race

100-12 = 88m

He travels at a constant speed for 88m

S = ut + 1/2 (at²)

But a = 0

S = ut

88 = 10.5t

t = 88/10.5

t = 8.38. seconds

Total time = 2.286 + 8.381

Total time = 10.667 seconds