| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 19 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Multi-stage motion with velocity-time graph given |
| Difficulty | Moderate -0.3 This is a straightforward M1 kinematics question requiring standard techniques: reading speed-time graphs, calculating areas under graphs, finding constant acceleration, and basic integration. Part (vi) involves integrating a quadratic which is slightly more involved than typical, but all parts follow routine procedures with no novel problem-solving required. Slightly easier than average due to clear structure and standard methods throughout. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
In this question take $g$ as $10\text{ m s}^{-2}$.
A small ball is released from rest. It falls for 2 seconds and is then brought to rest over the next
5 seconds. This motion is modelled in the speed-time graph Fig. 6.
\includegraphics{figure_4}
For this model,
\begin{enumerate}[label=(\roman*)]
\item calculate the distance fallen from $t = 0$ to $t = 7$, [3]
\item find the acceleration of the ball from $t = 2$ to $t = 6$, specifying the direction, [3]
\item obtain an expression in terms of $t$ for the downward speed of the ball from $t = 2$ to $t = 6$, [3]
\item state the assumption that has been made about the resistance to motion from $t = 0$ to $t = 2$. [1]
\end{enumerate}
The part of the motion from $t = 2$ to $t = 7$ is now modelled by $v = -\frac{3}{2}t^2 + \frac{19}{2}t + 7$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{4}
\item Verify that $v$ agrees with the values given in Fig. 6 at $t = 2$, $t = 6$ and $t = 7$. [2]
\item Calculate the distance fallen from $t = 2$ to $t = 7$ according to this model. [7]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI M1 Q4 [19]}}