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 placed velocity v1. If after first sliding on the belt the sphere is to have no linear velocity relative to the ground as it starts rolling on the belt without sliding, determine in terms of v1 and the coefficient of kinetic friction μk between the sphere and the belt

(a) The required value of v0,

(b) Time t1 at which the sphere will start rolling on the belt,

(c) The distance the sphere will have moved relative to the ground at time t1.

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