| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Displacement-time graph interpretation or sketching |
| Difficulty | Easy -1.2 This is a straightforward mechanics question requiring only basic interpretation of a velocity-time graph: finding distances by calculating areas of simple geometric shapes (rectangles/trapeziums) and sketching the corresponding displacement graph. It tests fundamental understanding with no problem-solving complexity or novel insight required. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| When \(t=4\), \(s=\frac{1}{2}\times 4\times 10\), \(s=20\) | B1 | Finding the area of the triangle or equivalent |
| When \(t=18\), \(s=\frac{1}{2}\times(18+12)\times 10\) | M1 | A complete method of finding the area of the trapezium or equivalent |
| \(s=150\) | A1 | CAO |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Graph joining \((0,0)\), \((4,20)\) and \((18,150)\) | B1 | Allow FT for their \((4,20)\) and \((18,150)\). Condone extension to \((20,150)\) with a horizontal line |
| The graph goes through \((16,140)\) | B1 | Allow SC1 for first two marks if there is a consistent displacement from a correct scale, e.g. plotting \((18,150)\) at \((19,150)\) |
| Curves at both ends | B1 | The sections from \(t=0\) to \(t=4\) and from \(t=16\) to \(t=18\) are both curves |
| [3] |
# Question 1:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| When $t=4$, $s=\frac{1}{2}\times 4\times 10$, $s=20$ | B1 | Finding the area of the triangle or equivalent |
| When $t=18$, $s=\frac{1}{2}\times(18+12)\times 10$ | M1 | A complete method of finding the area of the trapezium or equivalent |
| $s=150$ | A1 | CAO |
| **[3]** | | |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Graph joining $(0,0)$, $(4,20)$ and $(18,150)$ | B1 | Allow FT for their $(4,20)$ and $(18,150)$. Condone extension to $(20,150)$ with a horizontal line |
| The graph goes through $(16,140)$ | B1 | Allow SC1 for first two marks if there is a consistent displacement from a correct scale, e.g. plotting $(18,150)$ at $(19,150)$ |
| Curves at both ends | B1 | The sections from $t=0$ to $t=4$ and from $t=16$ to $t=18$ are both curves |
| **[3]** | | |
---1 Fig. 1 shows the velocity-time graph of a cyclist travelling along a straight horizontal road between two sets of traffic lights. The velocity, $v$, is measured in metres per second and the time, $t$, in seconds. The distance travelled, $s$ metres, is measured from when $t = 0$.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{63a2dc41-5e8b-4275-8653-ece5067c4306-2_732_1116_513_477}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
(i) Find the values of $s$ when $t = 4$ and when $t = 18$.\\
(ii) Sketch the graph of $s$ against $t$ for $0 \leqslant t \leqslant 18$.
\hfill \mbox{\textit{OCR MEI M1 2014 Q1 [6]}}