| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Given acceleration function find velocity |
| Difficulty | Standard +0.3 This is a standard M3 variable acceleration problem requiring the chain rule (v dv/dx = a) to find velocity as a function of displacement, then solving v=0. It's slightly above average difficulty due to being Further Maths content and requiring integration, but follows a well-practiced technique with straightforward algebra. |
| Spec | 6.06a Variable force: dv/dt or v*dv/dx methods |
\begin{enumerate}
\item A particle $P$ moves on the positive $x$-axis. When the displacement of $P$ from $O$ is $x$ metres, its acceleration is $( 6 - 4 x ) \mathrm { m } \mathrm { s } ^ { - 2 }$, measured in the direction of $x$ increasing. Initially $P$ is at $O$ and the velocity of $P$ is $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in the direction $O x$.
\end{enumerate}
Find the distance of $P$ from $O$ when $P$ is instantaneously at rest.\\
\hfill \mbox{\textit{Edexcel M3 Q1 [6]}}