Question

The cheetah is one of the fastest accelerating animals, for it can go from rest to 31.9 m/s in 4.16 s. If its mass is 113 kg, determine the average power developed by the cheetah during the acceleration phase of its motion. Express your answer in (a) watts and (b) horsepower.

Answer 1

P = Fv only is good for the instantaneous velocity and power, not the average power.

Average power would be Pav = total energy used/total time.
Total energy would be force x total distance, where total distance would be 0.5 a t^2, where t is the time required, 4.16 s,and a is the acceleration a = v/t = 7.67 m/s^2
So, total distance, xf, =0.5(7.67)(4.16)^2 = 66.4 m.
The force required is F = m a = 113(7.67) = 866.71 N

Energy used = F(xf) = 866.71(66.4) = 57549.544 J
and the average power is 57549.544/4.16 = 13834.025 W or 13834.025/746 = 18.54 hp