Answer to Question #179377 in Physics for Heizel Jean M. Barbas

Question

Cheetahs are considered as the fastest land animal. One cheetah observed in the

wild started running from rest and increased its velocity uniformly until it reached

99 km/h. It covered 40 m while running. What is its acceleration? How much time

will it take to cover the said displacement?

Answer 1

By definition, the acceleration is:

$$a = \dfrac{v_f - v_i}{t} = \dfrac{v_f}{t}$$

where $v_f = 99km/h = 27.5 m/s$ is the final speed, $v_i = 0$ is the initial speed, and $t$ is the time of accelration.

The displacement is given as follows:

$$d =v_it + \dfrac{a t^2}{2} = \dfrac{a t^2}{2}$$

Substituting the expression for $a$ and $d = 40m$ and expressing $t$, obtain:

$$d = \dfrac{v_ft}{2}\\ t = \dfrac{2d}{v_f} = \dfrac{2\cdot 40m}{27.5m/s} \approx 2.9s$$

Substituting the expression for $t$ into the formula for $a$, obtain:

$$a = \dfrac{v_f}{\dfrac{2d}{v_f}} = \dfrac{v_f^2}{2d}\\ a = \dfrac{(27.5m/s)^2}{2\cdot 40m} \approx 9.5m/s^2$$

Answer. The acceleration is 9.5 m/s^2, the time is 2.9s.