Suppose that Secretariat ran the Kentucky Derby with times of 25.5 s, 23.5 s, 23

Question

Suppose that Secretariat ran the Kentucky Derby with times of 25.5 s, 23.5 s, 23.6 s, and 23.8 s, for the quarter mile.

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

(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 -a quarter mile is 5280ft / 4 = 1320ft

1320ft / 25.5s = 51.8ft/s
1320ft / 23.5s = 56.170ft/s
1320ft / 23.6s = 55.9322ft/s
1320ft / 23.8s = 55.4621ft/s

(b)
if v = velocity, u = initial velocity, a = acceleration, and t = time
v = u + a*t

Using the calculated value,
55.462ft/s = 0 + a*23.8s
a = 2.3303ft/s^2

Using your value,
60.0ft/s = 0 + a*22.5s
a = 2.33ft/s^2

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