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

Answer

`[oo,v=v_(0)-(rs)/(m')(mv_(0))/(r'),(v_(0)(eta-1))/(ln(eta))]`