Answer to Question #4146 in Mechanics | Relativity for Jp

Question

A world class sprinter can reach top speed, 11.5m/s, in the first 15.0m of a race. What is the average deceleration of this sprinter and how long does it take her to reach that speed?

Answer 1

Using the equations of the motion, we can write
h = v₀t+ at²/2, where h is the covered distance, h₀ is the initial position, v₀ is the initial speed, a is the acceleration, t is the time.
Since h₀ = 0, v₀ = 0,
h = at²/2.
t² = 2h/a.
t = √2h/a
v = v0 + at = v0 + a*√2h/a = √2ha
v = √2ha
v² = 2ha
a = v²/2h
a = 11.5²/(2*15) = 4.4 m/s².
t = √(2*15/4.4) = 2.61 s.