OCR H240/03 2022 June — Question 9 6 marks

Exam BoardOCR
ModuleH240/03 (Pure Mathematics and Mechanics)
Year2022
SessionJune
Marks6
PaperDownload PDF ↗
TopicConstant acceleration (SUVAT)
TypeTwo vehicles: overtaking or meeting (graph-based)
DifficultyModerate -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.
Spec3.02b 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.
  1. Calculate the deceleration of car \(A\). [2]
  2. Determine the value of \(t\) when \(B\) overtakes \(A\). [4]

\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]}}