| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Maximum speed on incline vs horizontal |
| Difficulty | Standard +0.3 This is a standard M2 power-force-velocity question requiring the formula P=Fv and Newton's second law. Parts (a) and (b) are routine textbook exercises; part (c) adds an incline component but follows the same method. The multi-step nature and inclusion of an incline elevates it slightly above average difficulty, but it requires no novel insight—just systematic application of well-practiced techniques. |
| Spec | 6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(25000 = 15(900 + 850a)\) | M1 A1 A1 | \(a = 0.902 \text{ ms}^{-2}\) |
| (b) \(25000 = 900v_{\text{max}}\) | M1 A1 A1 | \(v_{\text{max}} = 27.8 \text{ ms}^{-1}\) |
| (c) \(25000 = v(85g + 900)\) | M1 A1 M1 A1 | \(v = 14.4 \text{ ms}^{-1}\) |
**(a)** $25000 = 15(900 + 850a)$ | M1 A1 A1 | $a = 0.902 \text{ ms}^{-2}$
**(b)** $25000 = 900v_{\text{max}}$ | M1 A1 A1 | $v_{\text{max}} = 27.8 \text{ ms}^{-1}$
**(c)** $25000 = v(85g + 900)$ | M1 A1 M1 A1 | $v = 14.4 \text{ ms}^{-1}$
**Total: 10 marks**
---A small car, of mass 850 kg, moves on a straight horizontal road. Its engine is working at its maximum rate of 25 kW, and a constant resisting force of magnitude 900 N opposes the car's motion.
\begin{enumerate}[label=(\alph*)]
\item Find the acceleration of the car when it is moving with speed 15 ms$^{-1}$. [3 marks]
\item Find the maximum speed of the car on the horizontal road. [3 marks]
\end{enumerate}
With the engine still working at 25 kW and the non-gravitational resistance remaining at 900 N, the car now climbs a hill inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = \frac{1}{10}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the maximum speed of the car on this hill. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q5 [10]}}