| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Velocity from two position vectors |
| Difficulty | Moderate -0.8 This is a straightforward M1 mechanics question requiring only basic vector operations: (a) finding speed from velocity using Pythagoras, and (b) using the constant velocity equation r = r₀ + vt with simple rearrangement. Both parts are direct applications of standard formulas with no problem-solving insight required. |
| Spec | 1.10c Magnitude and direction: of vectors1.10e Position vectors: and displacement |
| Answer | Marks | Guidance |
|---|---|---|
| \(v = \sqrt{2^2 + (-3)^2} = \sqrt{13} = 3.61 \text{ ms}^{-1}\) | M1 A1 (2) | M1 for \(\sqrt{\text{(sum of squares of components)}}\), allow \(\sqrt{2^2+3^2}\); A1 for \(\sqrt{13}\), 3.6 or better |
| Answer | Marks | Guidance |
|---|---|---|
| \(\mathbf{a} + 4(2\mathbf{i} - 3\mathbf{j}) = (\mathbf{i} - 4\mathbf{j})\) | M1 A1 | First M1 for \(\mathbf{a} \pm 4(2\mathbf{i}-3\mathbf{j}) = (\mathbf{i}-4\mathbf{j})\) oe; A1 for correct equation oe |
| \(\mathbf{a} = (-7\mathbf{i} + 8\mathbf{j})\) m | DM1 A1 (4) | DM1 dependent for solving for \(\mathbf{a}\); A1 for \((-7\mathbf{i}+8\mathbf{j})\); A0 for \(\begin{pmatrix}-7\mathbf{i}\\8\mathbf{j}\end{pmatrix}\) or \((-7\mathbf{i}, 8\mathbf{j})\) |
## Question 2:
### Part (a):
$v = \sqrt{2^2 + (-3)^2} = \sqrt{13} = 3.61 \text{ ms}^{-1}$ | M1 A1 (2) | M1 for $\sqrt{\text{(sum of squares of components)}}$, allow $\sqrt{2^2+3^2}$; A1 for $\sqrt{13}$, 3.6 or better
### Part (b):
$\mathbf{a} + 4(2\mathbf{i} - 3\mathbf{j}) = (\mathbf{i} - 4\mathbf{j})$ | M1 A1 | First M1 for $\mathbf{a} \pm 4(2\mathbf{i}-3\mathbf{j}) = (\mathbf{i}-4\mathbf{j})$ oe; A1 for correct equation oe
$\mathbf{a} = (-7\mathbf{i} + 8\mathbf{j})$ m | DM1 A1 (4) | DM1 dependent for solving for $\mathbf{a}$; A1 for $(-7\mathbf{i}+8\mathbf{j})$; A0 for $\begin{pmatrix}-7\mathbf{i}\\8\mathbf{j}\end{pmatrix}$ or $(-7\mathbf{i}, 8\mathbf{j})$
---2. A particle $P$ is moving with constant velocity ( $2 \mathbf { i } - 3 \mathbf { j }$ ) $\mathrm { m } \mathrm { s } ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Find the speed of $P$.
The particle $P$ passes through the point $A$ and 4 seconds later passes through the point with position vector ( $\mathbf { i } - 4 \mathbf { j }$ ) m.
\item Find the position vector of $A$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2014 Q2 [6]}}