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. $\frac{1}{\mu }$
• D. $\frac{1}{\sqrt{\mu }}$

Answer 1

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

Force on the car,
$F=\mu R$
or $ma=\mu mg$ ($\therefore u=0$)
or $a=\mu g$
Now, from the 2nd equation of motion
$s=ut+\frac{1}{2}a{t}^2=0+\frac{1}{2}a{t}^2$ ($\therefore u=0$)
$\therefore t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2s}{\mu g}}$ or $t\propto \frac{1}{\sqrt{\mu }}$
Hence, the correct answer is option (d).