Question

A car starts from rest to cover distance $s$. The coefficient of kinetic friction between the road and tire is $\mu$. The minimum time in which the car cover the distance $s$ is proportional to

• A. $\mu$
• B. $\sqrt{\mu }$
• C. $\frac{1}{\mu }$
• D. $\frac{1}{\sqrt{\mu }}$

Answer 1

The correct option is D $\frac{1}{\sqrt{\mu }}$

From FBD,

$ma=f=\mu N$

$=\mu mg$

$\Rightarrow a=\mu g$

by using $S=ut+\frac{1}{2}a{t}^2$, we will get,
$s=0+\frac{1}{2}\mu g{t}^2$

$t^2=\frac{2s}{g\mu }$

$\therefore t\propto \frac{1}{\sqrt{\mu }}$