On a rough horizontal surface, a block of mass m is at rest. It suddenly receives a horizontal linear impulse J. How long it will continue to be in motion? Take g as the acceleration due to gravity and $\mu$ is the coefficient of kinetic friction.

• A

  $\frac{J}{2\mu mg}$

• B

  $\frac{J^2}{2\mu m^{2}g}$

• C

  $\frac{J}{\mu mg}$

• D

  $\frac{2J}{\mu mg}$