| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2008 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Newton's second law with vector forces (find acceleration or force) |
| Difficulty | Moderate -0.8 This is a straightforward M1 mechanics question requiring direct application of Newton's second law (F=ma), basic vector operations (magnitude, angle using tan), and constant acceleration kinematics (v=u+at). All parts are routine calculations with no problem-solving insight needed, making it easier than average but not trivial since it requires correct vector manipulation across multiple steps. |
| Spec | 1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication3.02e Two-dimensional constant acceleration: with vectors3.03d Newton's second law: 2D vectors3.03f Weight: W=mg |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\tan\theta = \frac{8}{6}\) giving \(\theta \approx 53°\) | M1 A1 | (2) |
| (b) \(\mathbf{F} = 0.4(6\mathbf{i} + 8\mathbf{j}) = (2.4\mathbf{i} + 3.2\mathbf{j})\) and \( | \mathbf{F} | = \sqrt{2.4^2 + 3.2^2} = 4\) |
| (c) \(\mathbf{v} = 9\mathbf{i} - 10\mathbf{j} + 5(6\mathbf{i} + 8\mathbf{j}) = 39\mathbf{i} + 30\mathbf{j} \text{ (ms}^{-1})\) | M1 A1 A1 | (3) [8] |
**(a)** $\tan\theta = \frac{8}{6}$ giving $\theta \approx 53°$ | M1 A1 | (2)
**(b)** $\mathbf{F} = 0.4(6\mathbf{i} + 8\mathbf{j}) = (2.4\mathbf{i} + 3.2\mathbf{j})$ and $|\mathbf{F}| = \sqrt{2.4^2 + 3.2^2} = 4$ | M1 M1 A1 | (3) [The method marks can be gained in either order]
**(c)** $\mathbf{v} = 9\mathbf{i} - 10\mathbf{j} + 5(6\mathbf{i} + 8\mathbf{j}) = 39\mathbf{i} + 30\mathbf{j} \text{ (ms}^{-1})$ | M1 A1 A1 | (3) [8]
---3. A particle $P$ of mass 0.4 kg moves under the action of a single constant force $\mathbf { F }$ newtons. The acceleration of $P$ is $( 6 \mathbf { i } + 8 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }$. Find
\begin{enumerate}[label=(\alph*)]
\item the angle between the acceleration and $\mathbf { i }$,
\item the magnitude of $\mathbf { F }$.
At time $t$ seconds the velocity of $P$ is $\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }$. Given that when $t = 0 , \mathbf { v } = 9 \mathbf { i } - 10 \mathbf { j }$, (c) find the velocity of $P$ when $t = 5$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2008 Q3 [8]}}