A sprinter in a 100 dash accelerates uniformly from rest reaching a top speed of 14.7 m/s after 6.00 seconds. He then runs at constant speed for the remainder of the race.

B. How far did he travel in the first phase of the race?​

Respuesta :

I assume "first phase" refers to the first 6.00 seconds of the dash.

Since the sprinter starts from rest and accelerates uniformly, he covers a distance x after time t of

x = 1/2 at²

where a is his acceleration.

The sprinter's velocity v after time t is

v = at

so that if he attains a speed of 14.7 m/s after 6.00 s, he does so with acceleration a such that

14.7 m/s = a (6.00 s)   ⇒   a = 2.45 m/s²

Then in the first 6.00 seconds, the sprinter travels

x = 1/2 (2.45 m/s²) (6.00 s)² = 44.1 m