Question

A sphere of radius r and mass m has a linear velocity v0 directed to the left and no angular velocity as it is placed on a belt moving to the right with a constant velocity v1. If after sliding on the belt the sphere is to have no linear velocity relatives to the ground as it starts rolling on the belt without sliding. in terms of v1 and the coeefficient of kinetic friction mu k between the sphere and the belt. Determine- a. the required value of v0. b. the time t1 at which the sphere will start roling on the belt. and c. the distance the sphere will have moved relative to the ground at time t1 ?