Suppose that Secretariat ran the Kentucky Derby with times of 24.2 s, 23.5 s, 24
ID: 2025868 • Letter: S
Question
Suppose that Secretariat ran the Kentucky Derby with times of 24.2 s, 23.5 s, 24.9 s, and 22.6 s, for the quarter mile.(a) Find his average speed during each quarter-mile segment.
first segment 1 ft/s
second segment 2 ft/s
third segment 3 ft/s
fourth segment 4 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.)
5 ft/s2
Explanation / Answer
1.
Quarter Mile = 0.25 miles
Converting to Feet :
As 1 mile = 5280 ft
So,
0.25 mile = 5280 * 0.25 ft
= 1320 ft
This is the distance covered each time in different time intervals.
Average Speed = Total Distance Covered / Total Time Taken
For 1st Quarter mile,
d = 1320 ft
t = 24.2 s
So,
s = 1320 / 24.2
= 54.54 ft/s
For 2nd Quarter mile,
d = 1320 ft
t = 23.5 s
So,
s = 1320 / 23.5
= 56.17 ft/s
For 3rd Quarter mile,
d = 1320 ft
t = 24.9 s
So,
s = 1320 / 24.9
= 53.01 ft/s
For 4th Quarter mile,
d = 1320 ft
t = 22.6 s
So,
s = 1320 / 22.6
= 58.40 ft/s
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2.
Average Speed for the entire journey = (1320 * 4) / (24.2 + 23.5 + 24.9 + 22.6)
= 5280 / 95.2
= 55.46 ft/s
Average Acceleration for the entire journey = Average Speed / Total Time Taken
= 55.46 / 95.2
= 0.58 m/s2 Ans.
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