| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2021 |
| Session | June |
| Marks | 8 |
| 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 and solving when the i-component equals zero. All steps are routine applications of standard techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.02f Non-uniform acceleration: using differentiation and integration3.03d Newton's second law: 2D vectors |
2. A particle $P$ of mass 1.5 kg moves under the action of a single force $\mathbf { F }$ newtons.
At time $t$ seconds, $t \geqslant 0 , P$ has velocity $\mathbf { v } \mathrm { ms } ^ { - 1 }$, where
$$\mathbf { v } = \left( 5 t ^ { 2 } - t ^ { 3 } \right) \mathbf { i } + \left( 2 t ^ { 3 } - 8 t \right) \mathbf { j }$$
\begin{enumerate}[label=(\alph*)]
\item Find $\mathbf { F }$ when $t = 2$
At time $t = 0 , P$ is at the origin $O$.
\item Find the position vector of $P$ relative to $O$ at the instant when $P$ is moving in the direction of the vector $\mathbf { j }$
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2021 Q2 [8]}}