2. A vehicle of mass 450 kg is moving on a straight road that is inclined at angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 15 }\) At the instant when the vehicle is moving down the road at \(12 \mathrm {~ms} ^ { - 1 }\)

• the engine of the vehicle is working at a rate of \(P\) watts
• the acceleration of the vehicle is \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)
• the resistance to the motion of the vehicle is modelled as a constant force of magnitude \(R\) newtons

At the instant when the vehicle is moving up the road at \(12 \mathrm {~ms} ^ { - 1 }\)

• the engine of the vehicle is working at a rate of \(2 P\) watts
• the deceleration of the vehicle is \(0.5 \mathrm {~ms} ^ { - 2 }\)
• the resistance to the motion of the vehicle from non-gravitational forces is modelled as a constant force of magnitude \(R\) newtons

Find the value of \(P\).