A man\'s higher initial acceleration means that a man can outrun a horse over a

Question

A man's higher initial acceleration means that a man can outrun a horse over a very short race. A simple - but plausible - model for a sprint by a man and a horse uses the following assumptions: The man accelerates at 6.0 m/s2 for 1.8 s and then runs at a constant speed. A horse accelerates at a more modest 5.0 m/s2 but continues accelerating for 4.8 s and then continues at a constant speed. A man and a horse are competing in a 200 m race. The man is given a 100 m head start, so he begins 100 m from the finish line.

1.) How much time does the man take to complete the race?

2.) How much time does the horse take?

Explanation / Answer

Man acceleration am = 6.0m/s^2 for 1,8 s
Horse acceleration ah = 5.0m/s^2 for 4.8s
Head Start for man = 100m

1)
Inital Velocty of man u = 0
Final Velocity after acceleration = v = u + at
v = 0 + 6 * 1.8
v = 10.8m/s

Distance covered till man reaches this velocity =
s = ut + 0.5at^2
s = 0 + 0.5 *6*1.8^2
s = 9.72 m
Now, Man ,moves with constant velocity for distance = 100 - 9.72 = 90.28 m

S = u*t
90.28 = 10.8 * t
t = 90.28/10.8 s
t = 8.36 s

Time taken by man to complete the race = 8.36s + 1.8s
Time taken by man to complete the race = 10.16s

2)
Inital Velocty of horse u = 0
Final Velocity after acceleration = v = u + at
v = 0 + 5 * 4.8
v = 24m/s

Distance covered till horse reaches this velocity =
s = ut + 0.5at^2
s = 0 + 0.5 *5*4.8^2
s = 57.6 m
Now, Horse moves with constant velocity for distance = 200 - 57.6 = 142.4 m

S = u*t
142.4 = 24 * t
t = 142.4/24 s
t = 5.93 s

Toatl time taken by horse to complete the race = 5.93 s + 4.8s
Time taken by horse to complete the race = 10.73s

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