A car of mass $$\(600 \mathrm{~kg}\)$$ travels along a straight horizontal road with the engine of the car working at a constant rate of $$\(P\)$$ watts. The resistance to the motion of the car is modelled as a constant force of magnitude $$\(R\)$$ newtons. At the instant when the speed of the car is $$\(15 \mathrm{~ms}^{-1}\)$$, the magnitude of the acceleration of the car is $$\(0.2 \mathrm{~ms}^{-2}\)$$. Later the same car travels up a straight road inclined at angle $$\(\theta\)$$ to the horizontal, where $$\(\sin \theta=\frac{1}{20}\)$$. The resistance to the motion of the car from non-gravitational forces is modelled as a constant force of magnitude $$\(R\)$$ newtons. When the engine of the car is working at a constant rate of $$\(P\)$$ watts, the car has a constant speed of $$\(10 \mathrm{~m} \mathrm{~s}^{-1}\)$$. Find the value of $$\(P\)$$. (8)

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