Secretariat ran the 1.25 mi long Kentucky Derby with times of24.9 s, 24.3 s, 24.

Question

Secretariat ran the 1.25 mi long Kentucky Derby with times of24.9 s, 24.3 s, 24.1 s,22.6 s, and 22.6 s for each of the quarter mile segments. (a) Find his average speed during eachquarter-mile segment. first segment 1 ft/s second segment 2 ft/s third segment 3 ft/s fourth segment 4 ft/s fifth segment 5 ft/s
(b) Assuming that Secretariat's instantaneous speed at the finishline was the same as the average speed during the final quartermile, find his average acceleration for the entire race.(Hint: Recall that horses in the Derby start from rest,and use vf = vi +at.)
ft/s2 (a) Find his average speed during eachquarter-mile segment. first segment 1 ft/s second segment 2 ft/s third segment 3 ft/s fourth segment 4 ft/s fifth segment 5 ft/s
(b) Assuming that Secretariat's instantaneous speed at the finishline was the same as the average speed during the final quartermile, find his average acceleration for the entire race.(Hint: Recall that horses in the Derby start from rest,and use vf = vi +at.)
ft/s2 first segment 1 ft/s second segment 2 ft/s third segment 3 ft/s fourth segment 4 ft/s fifth segment 5 ft/s

Explanation / Answer

1 mile = 5280 ft, 1/4 mile = 1320 ft a) 1320 ft/24.9 s = 53.0 ft/s      1320 ft/24.3 s = 54.3 ft/s      1320 ft/24.1 s = 54.8 ft/s      1320 ft/22.6 s = 58.4 ft/s      1320 ft/22.6 s = 58.4 ft/s b) total time = 118.5 s initial speed = 0 final speed = 58.4 ft/s average acceleration = (58.4 - 0)/118.5 = 0.493ft/s2

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