Suppose that Secretariat ran the Kentucky Derby with times of 24.0 s, 23.8 s, 24

Question

Suppose that Secretariat ran the Kentucky Derby with times of 24.0 s, 23.8 s, 24.3 s, and 23.2 s, for the quarter mile.

(a) Find his average speed during each quarter-mile segment.
first segment 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

1/4 mi = 5280/4 = 1320 ft v1 = s1/t = 1320/24 = 55 ft/sec v2 = 1320/23.8 = 55.46 ft/sec v3 = 1320/24.3 = 54.32 ft/sec v4 = 1320/23.2 = 56.89 ft/sec b) v = a t where v is the final speed and t = 95.3 sec a = 56.89/95.3 = .597 ft/sec^2

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