Suppose that Secretariat ran the Kentucky Derby with times of 25.2 s, 24.0 s, 23
ID: 1686716 • Letter: S
Question
Suppose that Secretariat ran the Kentucky Derby with times of 25.2 s, 24.0 s, 23.6 s, and 23.5 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
Given distance is quarte mile
That is S=1/4 mi
= 5280 ft/4
= 1320 ft
During first segment
v1 = s1/t1
= 1320 ft/25.0s
= 52.8ft/sec
During second segment
v2 = s2/t2
= 1320 ft/23.6 s
= 55.93ft/sec
During third segment
v3 = s3/t 3
= 1320 ft/23.1s
= 57.14 ft/sec
During fourth segment
v4 = s4/t
= 1320 ft/22.90s
= 57.64 ft/sec
b)
v = a t where v is the final speed=57.64 ft/s
and t =t1+t2+t3+t4= 94.6 sec
a = 57.64 ft/sec/94.6 sec
= 0.609 ft/sec2
0.61 ft/sec2