| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2022 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (vectors) |
| Type | Find force using F=ma |
| Difficulty | Standard +0.3 This is a straightforward M2 mechanics question requiring differentiation of velocity to find acceleration, then applying F=ma, followed by integration to find position. While it involves trigonometric functions and vector notation, the techniques are standard and the question clearly signposts each step. Part (b) requires recognizing that parallel to i means the j-component of velocity equals zero, then solving a simple trigonometric equation. This is slightly above average difficulty due to the trigonometric manipulation and multi-step nature, but remains a routine M2 exercise. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10b Vectors in 3D: i,j,k notation3.02a Kinematics language: position, displacement, velocity, acceleration |
3. A particle $P$ of mass 0.25 kg is moving on a smooth horizontal surface under the action of a single force, $\mathbf { F }$ newtons.
At time $t$ seconds $( t \geqslant 0 )$, the velocity $\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }$ of $P$ is given by
$$\mathbf { v } = ( 6 \sin 3 t ) \mathbf { i } + ( 1 + 2 \cos t ) \mathbf { j }$$
\begin{enumerate}[label=(\alph*)]
\item Find $\mathbf { F }$ in terms of $t$.
At time $t = 0$, the position vector of $P$ relative to a fixed point $O$ is $( 4 \mathbf { i } - \sqrt { 3 } \mathbf { j } ) \mathrm { m }$.
\item Find the position vector of $P$ relative to $O$ when $P$ is first moving parallel to the vector $\mathbf { i }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2022 Q3 [9]}}