The force of resistance encountered by water on a motor boat of mass `m` going in still water with velocity `v` is proportional to the velocity `vdot` At `t=0` when its velocity is `v_0,` then engine shuts off. Find an expression for the position of motor boat at time `t` and also the distance travelled by the boat before it comes to rest. Take the proportionality constant as `k > 0.`