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

A block of mass m is pushed momentarily along a horizontal surfacewith

1.	A block of mass m is pushed momentarily along a horizontal surfacewith an initial velocity u. If mu_kis the coefficient of kinetic friction between the object and surface, find the time at which the block comes to rest.
Answer» SOLUTION : 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)`