Question

When the engine is switched off a vehicle of mass ${}^{\prime }{M}^{\prime }$ is moving on a rough horizontal road with momentum $P$. If the coefficient of friction between the road and tyres of the vehicle is ${\mu }_k$, the distance travelled by the vehicle before it comes to rest is

• A. $\frac{P^2}{2{\mu }_k{M}^{2}g}$
• B. $\frac{2{\mu }_k{M}^{2}g}{P^2}$
• C. $\frac{P^2}{2{\mu }_{k}g}$
• D. $\frac{P^2{M}^2}{2{\mu }_{k}g}$

Answer 1

The correct option is A $\frac{P^2}{2{\mu }_k{M}^{2}g}$

The initial kinetic energy the engine has with momentum $P=\frac{P^2}{2M}$

This kinetic energy converts completely into the work done against friction until the point the vehicle stops.

Thus $\frac{P^2}{2M}={\mu }_{k}MgS$

where $s$ is the distance traveled before it comes to rest.

$⟹S=\frac{P^2}{2{\mu }_k{M}^{2}g}$