| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Displacement expressions and comparison |
| Difficulty | Moderate -0.3 This is a straightforward two-particle SUVAT problem requiring students to set up distance equations for each car and solve a quadratic. The setup is clear, the algebra is routine, and the quadratic is given to verify, making it slightly easier than average for M1. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
3 Two cars, P and Q, are being crashed as part of a film 'stunt'.\\
At the start
\begin{itemize}
\item P is travelling directly towards Q with a speed of $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$,
\item Q is instantaneously at rest and has an acceleration of $4 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ directly towards P .\\
$P$ continues with the same velocity and $Q$ continues with the same acceleration. The cars collide $T$ seconds after the start.\\
(i) Find expressions in terms of $T$ for how far each of the cars has travelled since the start.
\end{itemize}
At the start, $P$ is 90 m from $Q$.\\
(ii) Show that $T ^ { 2 } + 4 T - 45 = 0$ and hence find $T$.
\hfill \mbox{\textit{OCR MEI M1 2011 Q3 [7]}}