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

Question #179377

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?


1
Expert's answer
2021-04-12T06:56:32-0400

By definition, the acceleration is:


a=vfvit=vfta = \dfrac{v_f - v_i}{t} = \dfrac{v_f}{t}

where vf=99km/h=27.5m/sv_f = 99km/h = 27.5 m/s is the final speed, vi=0v_i = 0 is the initial speed, and tt is the time of accelration.

The displacement is given as follows:


d=vit+at22=at22d =v_it + \dfrac{a t^2}{2} = \dfrac{a t^2}{2}

Substituting the expression for aa and d=40md = 40m and expressing tt, obtain:


d=vft2t=2dvf=240m27.5m/s2.9sd = \dfrac{v_ft}{2}\\ t = \dfrac{2d}{v_f} = \dfrac{2\cdot 40m}{27.5m/s} \approx 2.9s

Substituting the expression for tt into the formula for aa, obtain:


a=vf2dvf=vf22da=(27.5m/s)2240m9.5m/s2a = \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.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment