A world-class sprinter accelerates to his maximum speed in4.1 s. He then maintai

Question

A world-class sprinter accelerates to his maximum speed in4.1 s. He then maintains this speedfor the remainder of a 100-m race, finishing with a total time of10.2 s. (a) What is the runner's average accelerationduring the first 4.1 s?

(b) What is his average acceleration during the last 6.1 s?


(c) What is his average acceleration for the entire race?

(a) What is the runner's average accelerationduring the first 4.1 s?

(b) What is his average acceleration during the last 6.1 s?


(c) What is his average acceleration for the entire race?

Explanation / Answer

t = 4.1 s, T = 10.2 s, s = 100 m, a) a = average acceleration during t. v = maximum speed = at at2/2 + v(T - t) = s at2/2 + at(T - t) = s at(T - t/2) = s a = s/[t(T - t/2)] = 2.99 m/s2 b) during T - t = 6.1 s, v = constant a = 0 c) for entire race, initial velocity = 0, final = v = at average acceleration = v/T = at/T = 1.20 m/s2

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