| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 11 |
| 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 M1 kinematics question requiring standard techniques: differentiation to find acceleration, solving a linear equation, and integration to find displacement. The piecewise nature (accelerating then constant speed) is typical for M1, and all steps follow routine procedures with no novel problem-solving required. Slightly easier than average due to simple algebraic manipulation throughout. |
| Spec | 1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08d Evaluate definite integrals: between limits3.02f Non-uniform acceleration: using differentiation and integration |
A motorcyclist starts from rest at a point $O$ and travels in a straight line. His velocity after $t$ seconds is $v$ m s$^{-1}$, for $0 \leq t \leq T$, where $v = 7.2t - 0.45t^2$. The motorcyclist's acceleration is zero when $t = T$.
\begin{enumerate}[label=(\roman*)]
\item Find the value of $T$. [4]
\item Show that $v = 28.8$ when $t = T$. [1]
\end{enumerate}
For $t \geq T$ the motorcyclist travels in the same direction as before, but with constant speed $28.8$ m s$^{-1}$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Find the displacement of the motorcyclist from $O$ when $t = 31$. [6]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q3 [11]}}