A block of mass m is pushed momentarily along a horizontal surface with an initial velocity u. If `mu_k` is the coefficient of kinetic friction between the object and surface, find the time at which the block comes to rest.

Explanation

When the block slides, the force acting on the block is kinetic friction which is equal to `f_k = mu_s mg`.
From Newton.s second law ma= `-mu_s mg `
The negative sign implies that force acts on the opposite direction of motion. The acceleration of the block while sliding ` a = - mu_s g`
The negative sign implies that the acceleration is in opposite direction of the velocity. Note that the acceleration depends only on g and the coefficient of kinetic friction We can apply the following kinematic equation
v=u + at
The final velocity is zero.
`t = (u)/(mu_k g)`