Car Driving Up a Hill

Question

If a car is moving up a hill, there must be friction between the ground and the wheels. By describing how a thrust force is exerted on the car, explain why there must be friction.
Consider a car moving up a hill, where the gradient of the hill is 1/10. If the car is of mass m, what is the maximum velocity of the car given that the power output of the engine, P, is constant?
Create an expression for the velocity v at a time t. You don’t need to come to one final equation - create a set of differential equations.