| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Vector motion with components |
| Difficulty | Moderate -0.8 This is a straightforward integration question requiring students to integrate constant acceleration vectors and apply initial conditions. The calculation is routine (integrate -3i + 12j, add constant 4i, then find magnitude at t=0.5) with no conceptual challenges beyond basic mechanics definitions. Easier than average A-level due to minimal steps and standard technique. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02f Non-uniform acceleration: using differentiation and integration3.02g Two-dimensional variable acceleration |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(\mathbf{v} = 4\mathbf{i} + (-3\mathbf{i} + 12\mathbf{j})t\) | M1, A1 | Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(t = 0.5\), \(\mathbf{v} = 2.5\mathbf{i} + 6\mathbf{j}\) | B1\(\sqrt{}\) | \(\sqrt{}\) 2 terms and \(t\) substituted |
| \(\text{Speed} = \sqrt{2.5^2 + 6^2}\) | M1 | 2 terms |
| \(\text{Speed} = 6.5 \text{ ms}^{-1}\) | A1\(\sqrt{}\) | Total: 3 |
## Question 2:
### Part (a)
| Working | Marks | Guidance |
|---------|-------|----------|
| $\mathbf{v} = 4\mathbf{i} + (-3\mathbf{i} + 12\mathbf{j})t$ | M1, A1 | Total: 2 | use of $\mathbf{v} = \mathbf{u} + \mathbf{a}t$ |
### Part (b)
| Working | Marks | Guidance |
|---------|-------|----------|
| $t = 0.5$, $\mathbf{v} = 2.5\mathbf{i} + 6\mathbf{j}$ | B1$\sqrt{}$ | $\sqrt{}$ 2 terms and $t$ substituted |
| $\text{Speed} = \sqrt{2.5^2 + 6^2}$ | M1 | 2 terms |
| $\text{Speed} = 6.5 \text{ ms}^{-1}$ | A1$\sqrt{}$ | Total: 3 | $\sqrt{}$ 2 terms |
---2 A particle $P$ moves with acceleration $( - 3 \mathbf { i } + 12 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }$. Initially the velocity of $P$ is $4 \mathbf { i } \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Find the velocity of $P$ at time $t$ seconds.
\item Find the speed of $P$ when $t = 0.5$.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2006 Q2 [5]}}