Use \(g=10\text{ m s}^{-2}\), except where an answer in terms of \(g\) is requested.

An 800 kg car moves on a straight road. At constant \(20\text{ m s}^{-1}\) on a horizontal section its engine power is \(P\text{ W}\). At constant \(12\text{ m s}^{-1}\) uphill, on a section inclined at \(\sin^{-1}0.15\), its power is also \(P\text{ W}\). On both sections a constant resistance \(R\text{ N}\) opposes motion.

(a) Find \(R,P\). [5]

(b) Find the acceleration uphill at \(10\text{ m s}^{-1}\) when the engine operates at 32 kW. [3]