| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Distance from velocity function using calculus |
| Difficulty | Moderate -0.3 This is a straightforward kinematics question requiring basic integration and differentiation. Part (i) is trivial arithmetic, part (ii) is standard integration with constant determination, and part (iii) involves differentiating to find acceleration then substituting back. All techniques are routine M1 procedures with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits3.02f Non-uniform acceleration: using differentiation and integration |
A cyclist travels along a straight road. Her velocity $v$ m s$^{-1}$, at time $t$ seconds after starting from a point $O$, is given by
$v = 2$ for $0 \leq t \leq 10$,
$v = 0.03t^2 - 0.3t + 2$ for $t \geq 10$.
\begin{enumerate}[label=(\roman*)]
\item Find the displacement of the cyclist from $O$ when $t = 10$. [1]
\item Show that, for $t \geq 10$, the displacement of the cyclist from $O$ is given by the expression $0.01t^3 - 0.15t^2 + 2t + 5$. [4]
\item Find the time when the acceleration of the cyclist is $0.6$ m s$^{-2}$. Hence find the displacement of the cyclist from $O$ when her acceleration is $0.6$ m s$^{-2}$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q4 [10]}}