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 $v\dot{}$ 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 $k>0.$

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