Moderate -0.3 This is a straightforward application of the power-force-velocity relationship (P = Fv) combined with Newton's second law on an incline. Students must find the driving force from power, resolve forces parallel to the slope (weight component and resistance), then apply F = ma. It's a standard M1 question requiring routine techniques with no novel insight, making it slightly easier than average.
A car of mass \(1150 \text{ kg}\) travels up a straight hill inclined at \(1.2°\) to the horizontal. The resistance to motion of the car is \(975 \text{ N}\). Find the acceleration of the car at an instant when it is moving with speed \(16 \text{ m s}^{-1}\) and the engine is working at a power of \(35 \text{ kW}\).
[4]
A car of mass $1150 \text{ kg}$ travels up a straight hill inclined at $1.2°$ to the horizontal. The resistance to motion of the car is $975 \text{ N}$. Find the acceleration of the car at an instant when it is moving with speed $16 \text{ m s}^{-1}$ and the engine is working at a power of $35 \text{ kW}$.
[4]
\hfill \mbox{\textit{CAIE M1 2010 Q1 [4]}}