Question

A world-class sprinter can burst out of the blocks to essentially top speed (of about 11.5 m/s) in the first 15.0 m of the race. What is the average acceleration of this sprinter, and how long does it take her to reach that speed?

Answer 1

Given:

$v_i=0\:\rm m/s$

$v_f=11.5\:\rm m/s$

$d=15.0\:\rm m$

The distance traveled by a car is given by

$$d=\frac{v_f^2-v_i^2}{2a}=\frac{v_f+v_i}{2}t$$

Hence, the acceleration of a car

$$a=\frac{v_f^2-v_i^2}{2d}=\rm\frac{11.5^2-0^2}{2*15.0}=4.41\:\rm m/s^2$$

The time of motion

$$t=\frac{2d}{v_f+v_i}=\rm\frac{2*15.0}{11.5+0}=2.61\:\rm s$$