A car of mass m is propelled by an engine that has a maximum power P. The engine produces a force , where v is the speed of the car. The motion of the car is opposed by a frictional force that is proportional to its velocity, , where c is a constant. If the car starts from rest and full power is applied and held, find

• a)the suitable form of Newton’s second law that describes the stated problem,
• b) the speed of the car as a function of time.
• c) What is the maximum (terminal) speed that the car can reach?