A car is moving on an inclined road with friction acting upon it. When it is moving up the road at a speed v the engine is working at power 3P and when it is moving down the road at v the engine is working at a power P. Find the value of P.

Incline is at θ where sin θ = 1/20 and mass of the car is 800kg and v is 12.5 m/s

Up the road: Power = Fv                              F = R + (800g)/20

                                             Power = (R + 40g)*25/2 = 3P …. P = (R + 40g)*25/6

Down the road: Power = Fv          F = R – (800g)/20

                                             Power = (R - 40g)*25/2 = P

Equate the equations:

(R + 40g)*25/6 = (R – 40g)*25/2

25R + 1000g = 75R – 3000g so R = 80g

Therefore P = (80g – 40g)*25/2 = 500g = 4900W