| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | SUVAT in 2D & Gravity |
| Type | Particle motion: 2D direction/bearing |
| Difficulty | Moderate -0.5 This is a straightforward 2D kinematics question requiring basic vector operations (substitution, magnitude calculation) and bearing/direction interpretation. Part (i) involves substituting t=2.5 and verifying equal components for 45° angle, then finding speed using Pythagoras. Part (ii) requires integrating velocity to find displacement and calculating bearing. All techniques are standard M1 procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.10c Magnitude and direction: of vectors1.10h Vectors in kinematics: uniform acceleration in vector form |
| Answer | Marks |
|---|---|
| B1 | Need not be in vector form |
| E1 | Accept diag and/or correct derivation of just \(\pm 45°\) |
| F1 | FT their \(\mathbf{v}\) |
Total: 3 marks
| Answer | Marks |
|---|---|
| M1 | Consideration of \(\mathbf{s}\) (const accn or integration) |
| A1 | Correct sub into uvast with \(\mathbf{u}\) and \(\mathbf{a}\). (If integration used it must be correct but allow no arb constant) |
| A1 | cao. CWO. |
| A1 |
Total: 4 marks
Question 1:
(i)
B1 | Need not be in vector form
E1 | Accept diag and/or correct derivation of just $\pm 45°$
F1 | FT their $\mathbf{v}$
Speed: $\sqrt{10^2 + 10^2} = 14.14...$
Answer: $14.1 \text{ m s}^{-1}$ (3 s.f.)
Total: 3 marks
(ii)
M1 | Consideration of $\mathbf{s}$ (const accn or integration)
A1 | Correct sub into uvast with $\mathbf{u}$ and $\mathbf{a}$. (If integration used it must be correct but allow no arb constant)
A1 | cao. CWO.
A1 |
Working: $\mathbf{s} = 2.5 \begin{pmatrix} -5 \\ 10 \end{pmatrix} + \frac{1}{2} \times 2.5^2 \times \begin{pmatrix} 6 \\ -8 \end{pmatrix} = \begin{pmatrix} 6.25 \\ 0 \end{pmatrix}$
Answer: $090°$
Total: 4 marks1 The velocity of a model boat, $\mathbf { v } \mathrm { m } \mathrm { s } ^ { 1 }$, is given by
$$\mathbf { v } = \binom { 5 } { 10 } + t \binom { 6 } { 8 }$$
where $t$ is the time in seconds and the vectors $\binom { 1 } { 0 }$ and $\binom { 0 } { 1 }$ are east and north respectively.\\
(i) Show that when $t = 2.5$ the boat is travelling south-east (i.e. on a bearing of $135 ^ { \circ }$ ). Calculate its speed at this time.
The boat is at a point O when $t = 0$.\\
(ii) Calculate the bearing of the boat from O when $t = 2.5$.
\hfill \mbox{\textit{OCR MEI M1 Q1 [7]}}