Question

A simple model for a person running the 100 m dash is to assume the sprinter runs with constant acceleration until reaching top speed, then maintains that speed through the finish line. If a sprinter reaches his top speed of 11.2 m/s in 2.14 s, what will be his total time?

Answer 1

Answer:

He will complete the race in total time of T = 10 s

Explanation:

Total distance moved by the sprinter in 2.14 s is given as

$s = \frac{(v_{in} + v_{f})}{2} time$

$s = \frac{(0 + 11.2)}{2} (2.14)$

$s = 11.98 m$

now the distance remaining to move

$d = 100 - 11.98 = 88 m$

now he will move with uniform maximum speed for the remaining distance

so we will have

$time = \frac{d}{v}$

$time = \frac{88}{11.2} = 7.86 s$

so the total time to complete the race is given as

$T = 7.86 + 2.14 = 10 s$