Answer to Question #248384 in Physics for jer

Question #248384

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?


1
Expert's answer
2021-10-08T09:22:41-0400

Given:

vi=0m/sv_i=0\:\rm m/s

vf=11.5m/sv_f=11.5\:\rm m/s

d=15.0md=15.0\:\rm m


The distance traveled by a car is given by


d=vf2vi22a=vf+vi2td=\frac{v_f^2-v_i^2}{2a}=\frac{v_f+v_i}{2}t

Hence, the acceleration of a car

a=vf2vi22d=11.5202215.0=4.41m/s2a=\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=2dvf+vi=215.011.5+0=2.61st=\frac{2d}{v_f+v_i}=\rm\frac{2*15.0}{11.5+0}=2.61\:\rm s


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