A motorboat of mass m moves along a lake with velocity vo. At the moment t = 0 the engine of the boat is shut down. Assuming the resistance of water to be proportional to the velocity of the boat F = -rv, find:
(a) How long the motorboat moved with the shutdown engine;
(b) The velocity of the motorboat as a function of the distance covered with the shutdown engine, as well as the total distance covered till the complete stop;
(c) The mean velocity of the motorboat over the time interval (beginning with the moment t = 0), during which its velocity decreases η times.