Answer to Question #137884 in Physics for Kay

Question

The cheetah can reach a top speed of 114 km/h (71 mi/h). While chasing its prey in a short sprint, a cheetah starts from rest and runs 45 m in a straight line, reaching a final speed of 72 km/h.

(a) Determine the cheetah’s average acceleration during the short sprint, and

(b) find its displacement at t = 3.5 s.

Answer 1

Given:

$v_i=0\:\rm m/s$

$v_f=72\:\rm km/hr=20\:\ m/s$

$d=45\:\rm m$

$t=3.5\:\rm s$

(a) the cheetah’s average acceleration

$$a=\frac{v_f^2-v_i^2}{2d}=\rm\frac{20^2-0^2}{2\times 45}=4.44\: m/s^2$$

(b) the cheetah’s displacement at time $t$

$$d=\frac{at^2}{2}=\rm \frac{4.44\times 3.5^2}{2}=27.2\: m$$