A solid sphere rolls without slipping on a rough horizontal floor, moving with a

After an elastic collision with a smooth vertical wall, the sphere's translational velocity reverses direction (becomes -v) while its angular velocity ω remains unchanged (clockwise, ω = v/R). Initially, the sphere slips because the velocity condition for rolling without slipping (v_cm = -ωR for leftward motion) is not satisfied. Friction from the rough floor acts to the right, providing a torque that reduces the clockwise angular velocity to zero and then reverses it, while also decelerating the leftward translational motion. Eventually, the sphere reaches a state where v_cm = -ωR (with ω anticlockwise), i.e., rolling without slipping. Thus, the sphere will roll without slipping only after some time.