Secretariat ran the Kentucky Derby with times of 25.4 s, 24.3 s,23.1 s, and 22.8

Question

Secretariat ran the Kentucky Derby with times of 25.4 s, 24.3 s,23.1 s, and 22.8 s, for the quarter mile. (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 (b) Assuming that Secretariat's instantaneous speed at the finishline was the same as his average speed during the final quartermile, find his average acceleration for the entire race. (Hint:Recall that horses in the Derby start from rest.)
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 (b) Assuming that Secretariat's instantaneous speed at the finishline was the same as his average speed during the final quartermile, find his average acceleration for the entire race. (Hint:Recall that horses in the Derby start from rest.)
ft/s2 first segment 1 ft/s second segment 2 ft/s third segment 3 ft/s fourth segment 4 ft/s

Explanation / Answer

(a) Find his average speed during eachquarter-mile segment.
each quarter mile = 5280/4=1320
1st 1320/25.4=51.97 ft/s
2nd 1320/24.3=54.31 ft/s
3rd 1320/23.1=57.14 ft/s
4th 1320/22.8=87.89 ft/s

(b) Assuming that Secretariat's instantaneous speed at the finishline was the same as his average speed during the final quartermile, find his average acceleration for the entire race. (Hint:Recall that horses in the Derby start from rest.)

so initial velocity=0
final=87.89
total time=25.4+24.3+23.1+22.8= 95.6

so acc=(87.89-0)/95.6=.919ft/s2

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