A car of mass 2000 kg moves up a rough inclined plane at a constant speed of 10 m/s. The incline makes an angle with the horizontal such that = 1 20 . If the constant frictional force acting on the car is 500 N, the power output of the car's engine is : ( g = 10 m/s ^2 )

Step-by-step solution

Since the car moves at a constant speed, its acceleration is zero, meaning the net force acting on it is zero. The driving force F provided by the engine must balance both the downward component of gravity along the incline and the opposing frictional force f . F = mg + f F = (2000 10 1 20 ) + 500 F = 1000 + 500 = 1500 N. The power output of the engine is given by the product of the driving force and the velocity. P = F v P = 1500 10 = 15000 W. P = 15 kW. Answer: 15 kW