| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Time to reach midpoint or specific position |
| Difficulty | Moderate -0.8 This is a straightforward SUVAT question requiring standard application of kinematic equations with given values. Parts (i)-(iii) involve direct substitution into formulas (v²=u²+2as, then finding t), while part (iv) requires only basic conceptual understanding that the car travels slower in the first half. No algebraic manipulation complexity or novel problem-solving insight needed. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(s = ut + \frac{1}{2}at^2\) | ||
| \(\frac{215}{2} = 12t + \frac{1}{2} \times 1.9 \times t^2\) | M1 | Selection and use of \(s = ut + \frac{1}{2}at^2\), oe. Correct elements but condone minor arithmetic errors. |
| \(t = \frac{-12 \pm \sqrt{12^2 + 4 \times 0.95 \times 107.5}}{1.9}\) | M1 | Use of quadratic formula (may be implied by answer), oe. |
| \(t = 6.055\) (or \(-18.69\)) | A1 | FT their \(a\) only. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(v^2 - u^2 = 2as\) and \(s = \frac{(u+v)}{2}t\) | ||
| \(v = \pm\sqrt{12^2 + 2 \times 1.9 \times 107.5} = (\pm)23.505...\) | M1 | Selection and use of a complete valid 2-stage method |
| \(s = \frac{(u+v)}{2}t \Rightarrow t = \frac{2 \times 107.5}{(12 + 23.505...)}\) or \(t = \frac{2 \times 107.5}{(12 - 23.505...)}\) | M1 | Using the output from the first stage to find \(t\) |
| \(t = 6.055\) (or \(18.69\)) | A1 | FT their \(a\) only. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Because it is accelerating, it travels less fast in the first half of the distance and so takes more time. | B1 | Answer must refer to the two parts of the distance. No credit for "Because it is accelerating" or "Because its speed is not uniform" alone. B1 awarded for "It is travelling faster between M and B than it is between A and M". |
## Question 1:
### Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $s = ut + \frac{1}{2}at^2$ | | |
| $\frac{215}{2} = 12t + \frac{1}{2} \times 1.9 \times t^2$ | M1 | Selection and use of $s = ut + \frac{1}{2}at^2$, oe. Correct elements but condone minor arithmetic errors. |
| $t = \frac{-12 \pm \sqrt{12^2 + 4 \times 0.95 \times 107.5}}{1.9}$ | M1 | Use of quadratic formula (may be implied by answer), oe. |
| $t = 6.055$ (or $-18.69$) | A1 | FT their $a$ only. |
**Alternative: 2-stage method**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $v^2 - u^2 = 2as$ and $s = \frac{(u+v)}{2}t$ | | |
| $v = \pm\sqrt{12^2 + 2 \times 1.9 \times 107.5} = (\pm)23.505...$ | M1 | Selection and use of a complete valid 2-stage method |
| $s = \frac{(u+v)}{2}t \Rightarrow t = \frac{2 \times 107.5}{(12 + 23.505...)}$ or $t = \frac{2 \times 107.5}{(12 - 23.505...)}$ | M1 | Using the output from the first stage to find $t$ |
| $t = 6.055$ (or $18.69$) | A1 | FT their $a$ only. |
### Part (iv)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Because it is accelerating, it travels less fast in the first half of the distance and so takes more time. | B1 | Answer must refer to the two parts of the distance. No credit for "Because it is accelerating" or "Because its speed is not uniform" alone. B1 awarded for "It is travelling faster between M and B than it is between A and M". |
---1 Fig. 4 illustrates a straight horizontal road. $A$ and $B$ are points on the road which are 215 metres apart and $M$ is the mid-point of AB .
When a car passes A its speed is $12 \mathrm {~ms} ^ { - 1 }$ in the direction AB . It then accelerates uniformly and when it reaches $B$ its speed is $31 \mathrm {~ms} ^ { - 1 }$.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{b9e41fac-9f4b-4165-af03-67ebdcb326de-1_140_1160_455_488}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{center}
\end{figure}
(i) Find the car's acceleration.\\
(ii) Find how long it takes the car to travel from A to B .\\
(iii) Find how long it takes the car to travel from A to M .\\
(iv) Explain briefly, in terms of the speed of the car, why the time taken to travel from A to M is more than half the time taken to travel from A to B .
\hfill \mbox{\textit{OCR MEI M1 Q1 [8]}}