A motorboat of mass m moves along a lake with velocity v0. 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.
Solution:
