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Answer to Question #4146 in Mechanics | Relativity for Jp

Question #4146
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?
Expert's answer
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.

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