Question

A car is moving along a straight horizontal road with a speed $v_0$. If the coefficient of friction between the tyres and the road is $\mu$, the shortest distance in which the car can be stopped is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A.

Given,

Initial velocty, $u=v_0$

Final velocity, $v=0$

Coefficient of friction = $\mu$

The retarding force between the tyres and the road is given by,

$F=ma=\mu R=\mu mg$

$\therefore a=\mu g$

Now from equation of motion $v^2=u^2-2as$
$\Rightarrow 0=u^2-2as$

$\Rightarrow s=\frac{u^2}{2a}=\frac{u^2}{2\mu g}=\frac{v_0^2}{2\mu g}$

$\therefore$ The shortest distance in which the car can be stopped is $\frac{v_0^2}{2\mu g}$.