| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Finding when particle at rest |
| Difficulty | Moderate -0.8 This is a straightforward kinematics question requiring differentiation of a cubic to find velocity, solving a quadratic equation, then substituting back. All steps are routine calculus applications with no problem-solving insight needed, making it easier than average but not trivial due to the algebraic manipulation required. |
| Spec | 1.07i Differentiate x^n: for rational n and sums3.02a Kinematics language: position, displacement, velocity, acceleration |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Velocity \(v\) is \(\frac{ds}{dt} = 3t^2 - 6t\) | M1 | Attempt to find \(\frac{ds}{dt}\) |
| \(= 0\) | M1 | \(\frac{ds}{dt} = 0\) must be stated |
| \(t = 0\) or \(2\) | A1 | Both roots found |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(s(0) = 3\) so distance \(3\) m | A1 | Accept seeing 3 without comment |
| \(s(2) = 8 - 12 + 3 = -1\) so distance is \(1\) m | A1 | \(-1\) for \(s\) must be seen as well as \(1\) m for distance |
# Question 5:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Velocity $v$ is $\frac{ds}{dt} = 3t^2 - 6t$ | M1 | Attempt to find $\frac{ds}{dt}$ |
| $= 0$ | M1 | $\frac{ds}{dt} = 0$ must be stated |
| $t = 0$ or $2$ | A1 | Both roots found |
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $s(0) = 3$ so distance $3$ m | A1 | Accept seeing 3 without comment |
| $s(2) = 8 - 12 + 3 = -1$ so distance is $1$ m | A1 | $-1$ for $s$ must be seen as well as $1$ m for distance |
---5 Particle P moves on a straight line that contains the point O .\\
At time $t$ seconds the displacement of P from O is $s$ metres, where $s = t ^ { 3 } - 3 t ^ { 2 } + 3$.
\begin{enumerate}[label=(\alph*)]
\item Determine the times when the particle has zero velocity.
\item Find the distances of P from O at the times when it has zero velocity.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 1 Q5 [5]}}