A car has mass 1000 kg. When the car is travelling at a steady speed of v m s⁻¹, where v > 2, the resistance to motion of the car is (Av + B) N, where A and B are constants. The car can travel along a horizontal road at a steady speed of 18 m s⁻¹ when its engine is working at 36 kW. The car can travel up a hill inclined at an angle of θ to the horizontal, where sin θ = 0.05, at a steady speed of 12 m s⁻¹ when its engine is working at 21 kW. Find A and B.

1. A car has mass 1000 kg. When the car is travelling at a steady speed of v m s⁻¹, where v > 2, the resistance to motion of the car is (Av + B) N, where A and B are constants. The car can travel along a horizontal road at a steady speed of 18 m s⁻¹ when its engine is working at 36 kW. The car can travel up a hill inclined at an angle of θ to the horizontal, where sin θ = 0.05, at a steady speed of 12 m s⁻¹ when its engine is working at 21 kW. Find A and B.[7]