A force `F=2t` is spplied at `t=0` sec to the block of mass m placed on a rough horizontal surface. The coefficient of static and kinetic friction between the block and surface are `mu_S` and `mu_k` rspectively. Which of the following graphs best represents the acceleration vs time of the block`(mu_Sgtmu_k)`?

Options

A.
B.
C.
D.

Answer

D

Explanation

Let `t_(0)` be the time when friction force is maximum
`F = 2t_(0) =mu_(S) mg`
The block just starts moves immediately after this instant, with acceleration
`=(mu_(S)mg-mu_(k)mg)/(m)=(mu_(S)-mu_(k))g`
For `t gt t_(o)` the acceleration of the block is
`a = (2t_(o)-mu_(k)mg)/(m)`