| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2009 |
| Session | June |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Piecewise motion functions |
| Difficulty | Moderate -0.3 This is a standard M1 kinematics question involving differentiation for acceleration, integration for displacement, and piecewise motion analysis. All parts follow routine procedures: (i) differentiate velocity, (ii) integrate to find distance, (iii-iv) apply constant velocity and SUVAT equations across different phases. The multi-part structure and bookwork marks make it slightly easier than average. |
| Spec | 1.08d Evaluate definite integrals: between limits3.02a Kinematics language: position, displacement, velocity, acceleration3.02f Non-uniform acceleration: using differentiation and integration |
\includegraphics{figure_7}
A sprinter $S$ starts from rest at time $t = 0$, where $t$ is in seconds, and runs in a straight line. For $0 \leq t \leq 3$, $S$ has velocity $(6t - t^2)$ m s$^{-1}$. For $3 < t \leq 22$, $S$ runs at a constant speed of $9$ m s$^{-1}$. For $t > 22$, $S$ decelerates at $0.6$ m s$^{-2}$ (see diagram).
\begin{enumerate}[label=(\roman*)]
\item Express the acceleration of $S$ during the first $3$ seconds in terms of $t$. [2]
\item Show that $S$ runs $18$ m in the first $3$ seconds of motion. [5]
\item Calculate the time $S$ takes to run $100$ m. [3]
\item Calculate the time $S$ takes to run $200$ m. [7]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 2009 Q7 [17]}}