| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Vector motion with components |
| Difficulty | Moderate -0.3 This is a straightforward M2 mechanics question requiring basic differentiation to find acceleration and integration to find position. Part (a) is routine verification (differentiate velocity to show constant acceleration), and part (b) involves standard integration of velocity components and calculating magnitude. The 8 total marks reflect multiple steps rather than conceptual difficulty, making it slightly easier than average for A-level. |
| Spec | 1.10c Magnitude and direction: of vectors3.02a Kinematics language: position, displacement, velocity, acceleration3.02b Kinematic graphs: displacement-time and velocity-time |
The velocity v m s$^{-1}$ of a particle $P$ at time $t$ seconds is given by
$$\mathbf{v} = (3t - 2)\mathbf{i} - 5t\mathbf{j}.$$
\begin{enumerate}[label=(\alph*)]
\item Show that the acceleration of $P$ is constant.
[2]
\end{enumerate}
At $t = 0$, the position vector of $P$ relative to a fixed origin $O$ is 3i m.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the distance of $P$ from $O$ when $t = 2$.
[6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q1 [8]}}