Standard +0.3 This is a straightforward mechanics problem requiring application of Newton's second law combined with the power equation P=Fv. Students must resolve forces parallel to the slope (weight component, resistance, driving force), use F=ma to find the driving force, then calculate power. It's slightly above average difficulty due to multiple steps and the inclined plane context, but follows a standard template with no novel insight required.
2 A train of mass 240000 kg travels up a slope inclined at an angle of \(4 ^ { \circ }\) to the horizontal. There is a constant resistance of magnitude 18000 N acting on the train. At an instant when the speed of the train is \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) its deceleration is \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). Find the power of the engine of the train.
2 A train of mass 240000 kg travels up a slope inclined at an angle of $4 ^ { \circ }$ to the horizontal. There is a constant resistance of magnitude 18000 N acting on the train. At an instant when the speed of the train is $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ its deceleration is $0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. Find the power of the engine of the train.\\
\hfill \mbox{\textit{CAIE M1 2018 Q2 [4]}}