Because it can go from rest to 7.4 m/s (about 17 mi/h) in 1.1 s, one of the fast

Question

Because it can go from rest to 7.4 m/s (about 17 mi/h) in 1.1 s, one of the fastest-accelerating animals is the cheetah. If its mass is 56.0 kg, determine the average power developed by the cheetah during the acceleration phase of its motion. Express your answer in the following units. (a) watts Can you write an expression for the average power of the cheetah in terms of the work done by the cheetah and the time over which this work is done? How does the work done by the cheetah compare to its change in kinetic energy? Can you write an expression for the change in kinetic energy of the cheetah in terms of its final and initial speed? W (b) horsepower hp

Explanation / Answer

a )

given

v = 7.4 m/s

t = 1.1 sec

u = 0

a = v - u / t

a = 7.4 / 1.1

a = 6.7272 m/sec2  

distance S = u t + 1/2 a t2

S = 0 + 0.5 X 6.7272 X 1.12

S = 4.0699 m

Power P = F .S / t

P = m X a X S / t

P = 56 X 6.7272 X 4.0699 / 1.1

P = 1393.841 W

b )

P = 1393.841 / 746

P = 1.8684 horse power

P = 1.8684 hp

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