| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Vector motion with components |
| Difficulty | Moderate -0.8 This is a straightforward M2 kinematics question requiring routine differentiation of position vectors and substitution. Part (a) involves simple simultaneous equations, part (b) requires finding velocity by differentiation and calculating magnitude, and part (c) asks for eliminating the parameter to sketch a parabola. All techniques are standard with no problem-solving insight needed, making it easier than average. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02a Kinematics language: position, displacement, velocity, acceleration |
| Answer | Marks |
|---|---|
| \(a(60°) = 90\) | M1 A1 A1 |
| \(a = \frac{1}{40}\) | |
| \(b(60) = 30\) | |
| \(b = \frac{1}{2}\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(v = \frac{1}{20}ti + \frac{1}{2}j\) | M1 A1 M1 A1 | |
| \(t = 60\): \(v = 3i + \frac{1}{2}j\) | ||
| \( | v | = 3.04 \, \text{ms}^{-1}\) |
| Answer | Marks | Guidance |
|---|---|---|
| Sketch of parabola between \((0, 0)\) and \((90, 30)\) | B2 | Total: 9 marks |
### (a)
$a(60°) = 90$ | M1 A1 A1 |
$a = \frac{1}{40}$ | |
$b(60) = 30$ | |
$b = \frac{1}{2}$ | |
### (b)
$v = \frac{1}{20}ti + \frac{1}{2}j$ | M1 A1 M1 A1 |
$t = 60$: $v = 3i + \frac{1}{2}j$ | |
$|v| = 3.04 \, \text{ms}^{-1}$ | |
### (c)
Sketch of parabola between $(0, 0)$ and $(90, 30)$ | B2 | **Total: 9 marks**A particle $P$ starts from the point $O$ and moves such that its position vector $\mathbf{r}$ m relative to $O$ after $t$ seconds is given by $\mathbf{r} = at^2\mathbf{i} + bt\mathbf{j}$.
60 seconds after $P$ leaves $O$ it is at the point $Q$ with position vector $(90\mathbf{i} + 30\mathbf{j})$ m.
\begin{enumerate}[label=(\alph*)]
\item Find the values of the constants $a$ and $b$. [3 marks]
\item Find the speed of $P$ when it is at $Q$. [4 marks]
\item Sketch the path followed by $P$ for $0 \leq t \leq 60$. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q4 [9]}}