Suppose that Secretariat ran the Kentucky Derby with times of 24.0 s, 24.5 s, 23

Question

Suppose that Secretariat ran the Kentucky Derby with times of 24.0 s, 24.5 s, 23.3 s, and 23.5 s, for the quarter mile.

(a) Find his average speed during each quarter-mile segment. first segment 1 ft/s
second segment ft/s
third segment ft/s
fourth segment ft/s

(b) Assuming that Secretariat's instantaneous speed at the finish line was the same as the average speed during the final quarter mile, find his average acceleration for the entire race. (Hint: Recall that horses in the Derby start from rest.)
ft/s2

Explanation / Answer

a) first segment average speed = 0.25* 5280/24 = 55ft/s 2nd segment average speed = 0.25*5280/24.5 = 53.9ft/s 3rd segment average speed = 0.25*5280/23.3 = 56.65ft/s 4th segment average speed = 0.25*5280/23.5 = 56.17ft/s b) total time taken = 95.3s final speed = 56.17ft/s initial speed = 0 so, average acceleration = 56.17/95.3 = 0.59ft/s2

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