| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Velocity from acceleration by integration |
| Difficulty | Moderate -0.3 This is a straightforward kinematics question requiring integration of acceleration to find velocity, then using given conditions to find the constant of integration. Part (b) involves solving a quadratic equation. While it requires multiple steps, the techniques are standard M2 material with no conceptual challenges or novel problem-solving required, making it slightly easier than average. |
| Spec | 3.02f Non-uniform acceleration: using differentiation and integration |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(v = \int a \, dt = 4t^2 - 18t + c\), \(v(3) = 2\): \(c = 20\), \(v = 4t^2 - 18t + 20\) | M1 A1 M1 A1 | |
| (b) \(v = 0\): \(2(t-2)(2t-5) = 0\), \(t = 2, t = 2.5\) | M1 A1 A1 | Total: 7 marks |
(a) $v = \int a \, dt = 4t^2 - 18t + c$, $v(3) = 2$: $c = 20$, $v = 4t^2 - 18t + 20$ | M1 A1 M1 A1 |
(b) $v = 0$: $2(t-2)(2t-5) = 0$, $t = 2, t = 2.5$ | M1 A1 A1 | Total: 7 marksThe acceleration of a particle $P$ is $(8t - 18)$ ms$^{-2}$, where $t$ seconds is the time that has elapsed since $P$ passed through a fixed point $O$ on the straight line on which it is moving.
At time $t = 3$, $P$ has speed $2$ ms$^{-1}$. Find
\begin{enumerate}[label=(\alph*)]
\item the velocity of $P$ at time $t$, [4 marks]
\item the values of $t$ when $P$ is instantaneously at rest. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q1 [7]}}