Q. 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) $1/\mu$
D) $1/\sqrt{\mu}$
Explanation
(d) Force on the car
$F = \mu R$
or $ma = \mu mg$ ($\because R = mg$)
or $a = \mu g$
Now from 2nd equation of motion
$s = ut + \frac{1}{2}at^{2}$
or $s = 0 + \frac{1}{2}at^{2}\ \ \ (\because u = 0)$
or $t = \sqrt{\frac{2s}{\mu g}}$
$\therefore\ t = \sqrt{\frac{2s}{\mu g}}$
or $t \propto \ \frac{1}{\sqrt{\mu}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.