| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2022 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Two vehicles: overtaking or meeting (graph-based) |
| Difficulty | Moderate -0.3 This is a straightforward kinematics problem using constant acceleration equations and velocity-time graph interpretation. Part (a) requires simple application of v = u + at. Part (b) involves comparing areas under the graph (distances travelled), which is a standard technique but requires careful setup of the equation. The problem is slightly easier than average due to its routine nature and clear structure, though the multi-step calculation in part (b) prevents it from being trivial. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
\includegraphics{figure_9}
The diagram shows a velocity-time graph representing the motion of two cars $A$ and $B$ which are both travelling along a horizontal straight road. At time $t = 0$, car $B$, which is travelling with constant speed $12 \mathrm{m s}^{-1}$, is overtaken by car $A$ which has initial speed $20 \mathrm{m s}^{-1}$.
From $t = 0$ car $A$ travels with constant deceleration for 30 seconds. When $t = 30$ the speed of car $A$ is $8 \mathrm{m s}^{-1}$ and the car maintains this speed in subsequent motion.
\begin{enumerate}[label=(\alph*)]
\item Calculate the deceleration of car $A$. [2]
\item Determine the value of $t$ when $B$ overtakes $A$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2022 Q9 [6]}}