When the engine is switched off, a vehicle of mass $M$ is moving on a rough horizontal road with momentum $p$. If the coefficient of friction between the road and the tyres of the vehicle is $\mu_k$, what is the distance travelled by the vehicle before it comes to rest?

• 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
  $\frac{p^2 M^2}{2 \mu_k g}$