| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2020 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Difficulty | Moderate -0.3 This is a straightforward kinematics question using calculus. Part (a) is immediate substitution. Part (b) requires differentiating to find acceleration, then solving two simultaneous equations—standard A-level technique. Part (c) is direct integration of a quadratic. All steps are routine with no problem-solving insight required, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02f Non-uniform acceleration: using differentiation and integration |
A car is travelling on a straight horizontal road. The velocity of the car, $v$ ms$^{-1}$, at time $t$ seconds as it travels past three points, $P$, $Q$ and $R$, is modelled by the equation
$v = at^2 + bt + c$,
where $a$, $b$ and $c$ are constants.
The car passes $P$ at time $t = 0$ with velocity $8$ ms$^{-1}$.
\begin{enumerate}[label=(\alph*)]
\item State the value of $c$. [1]
The car passes $Q$ at time $t = 5$ and at that instant its deceleration is $0.12$ ms$^{-2}$. The car passes $R$ at time $t = 18$ with velocity $2.96$ ms$^{-1}$.
\item Determine the values of $a$ and $b$. [4]
\item Find, to the nearest metre, the distance between points $P$ and $R$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2020 Q8 [7]}}