| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (vectors) |
| Type | When moving parallel to given vector |
| Difficulty | Moderate -0.3 This is a straightforward mechanics question requiring differentiation of position to find velocity (standard M2 technique), then solving when the velocity vector is parallel to i+j by equating component ratios. The algebra is simple and the method is routine textbook material, making it slightly easier than average. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors3.02a Kinematics language: position, displacement, velocity, acceleration3.02f Non-uniform acceleration: using differentiation and integration |
3. At time $t$ seconds, a particle $P$ has position vector $\mathbf { r }$ metres relative to a fixed origin $O$, where
$$\mathbf { r } = \left( t ^ { 3 } - 3 t \right) \mathbf { i } + 4 t ^ { 2 } \mathbf { j } , t \geq 0$$
Find
\begin{enumerate}[label=(\alph*)]
\item the velocity of $P$ at time $t$ seconds,
\item the time when $P$ is moving parallel to the vector $\mathbf { i } + \mathbf { j }$.\\
(5)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q3 [7]}}