Question

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

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

Answer 1

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

We know that,
The force is given by Newton's law as:

$ma=f=\mu N=\mu mg$

$\Rightarrow a=\mu g$

By using equation of motion,

$S=ut+\frac{1}{2}a{t}^2$ ,

we will get,

$s=0+\frac{1}{2}\mu g{t}^2$

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

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

Hence , option $\left(D\right)$ is correct.