Question

The cheetah is one of the fastest accelerating animals, for it can go from rest to 29.4 m/s in 5.35 s. If its mass is 101 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

8159 W, 10.9 hp

Step-by-step explanation:

The work done by the cheetah is equal to the kinetic energy gained, so we can write:

`W=\Delta K=(1)/(2)mv^2-(1)/(2)mu^2`

where

m = 101 kg is the mass of the cheetah

u = 0 is the initial speed

v = 29.4 m/s is the final speed

Substituting,

`W=(1)/(2)(101)(29.4)^2-0=43650 J`

Now we can calculate the power developed by the cheetah, given by:

`P=(W)/(t)`

where

t = 5.35 s

is the time taken. Substituting,

`P=(43650)/(5.35)=8159 W`

And keeping in mind that

1 hp = 746 W

We can also convert into horsepowers:

`P=(8159)/(746)=10.9 hp`