| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2011 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Find steady/maximum speed given power |
| Difficulty | Moderate -0.8 This is a straightforward application of the power-force-velocity relationship (P=Fv) for part (a), requiring only one step to find maximum speed when driving force equals resistance. Part (b) uses F=ma with P=Fv to find acceleration at a given speed - standard M2 bookwork with no problem-solving insight needed, making it easier than average. |
| Spec | 3.03d Newton's second law: 2D vectors6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Constant speed \(\Rightarrow\) Driving force = resistance, \(F = 32\) | B1 | |
| \(P = F \times v \Rightarrow 32v = 384\) | M1 | |
| \(v = 12 \text{ ms}^{-1}\) | A1 | |
| (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P = F \times v \Rightarrow 384 = F \times 9,\ F = \frac{384}{9}\) | M1 | |
| Their \(F - 32 = 120a\) | M1 | |
| \(a = 0.089 \text{ ms}^{-2}\) | A1 | |
| (3) [6] |
## Question 1:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Constant speed $\Rightarrow$ Driving force = resistance, $F = 32$ | B1 | |
| $P = F \times v \Rightarrow 32v = 384$ | M1 | |
| $v = 12 \text{ ms}^{-1}$ | A1 | |
| | **(3)** | |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P = F \times v \Rightarrow 384 = F \times 9,\ F = \frac{384}{9}$ | M1 | |
| Their $F - 32 = 120a$ | M1 | |
| $a = 0.089 \text{ ms}^{-2}$ | A1 | |
| | **(3) [6]** | |
---\begin{enumerate}
\item A cyclist starts from rest and moves along a straight horizontal road. The combined mass of the cyclist and his cycle is 120 kg . The resistance to motion is modelled as a constant force of magnitude 32 N . The rate at which the cyclist works is 384 W . The cyclist accelerates until he reaches a constant speed of $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\end{enumerate}
Find\\
(a) the value of $v$,\\
(b) the acceleration of the cyclist at the instant when the speed is $9 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
\hfill \mbox{\textit{Edexcel M2 2011 Q1 [6]}}