Question

A cheetah, mass M, is initially at rest at time t=0. After spotting prey, it begins to run straight toward it. The cheetah's legs apply constant power P, all of which power goes into increasing its kinetic energy. a) Determine the speed of the cheetah as a function of time t (writing in terms of t, M, P). Hint: the cheetah is undergoing constant power motion, not constant acceleration motion. b) Is the magnitude of the force supplied by the cheetah's legs greater right after t=0 or at a later time?

Answer 1

Answer: a. $v=\sqrt{ \frac{2P\times t}{m}}$

b. The magnitude of the force supplied by the cheetah's legs greater right after t=0

Explanation:

We know:

Kinetic Energy

$K.E.= \frac{1}{2} m.v^2$

where:

m= mass of the body

v= velocity of the body

also,

Power, P= rate of energy or work.

So, if the Cheetah's leg produce power P for time t then the kinetic energy of the Cheetah will be given as:

$K.E.= P\times t$

$\Rightarrow \frac{1}{2}m.v^2=P\times t$

$v=\sqrt{ \frac{2P\times t}{m}}$

The magnitude of the force produced by the legs of the cheetah is greater just after time t=0 because it has spent a fraction of second using its energy.