| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2017 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Variable force (position x) - find velocity |
| Difficulty | Standard +0.8 This M3 question requires setting up and solving a differential equation using v dv/dx = a for variable force motion on an incline. Students must correctly combine the component of weight down the plane (mg sin 30°) with the resistance force (½mx²), integrate to find v², then solve for when v=0. While the integration is straightforward, the setup requires careful force analysis and the method is less routine than standard constant acceleration problems. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.06a Variable force: dv/dt or v*dv/dx methods |
\begin{enumerate}
\item A particle $P$ of mass $m \mathrm {~kg}$ is initially held at rest at the point $O$ on a smooth plane which is inclined at $30 ^ { \circ }$ to the horizontal. The particle is released from rest and slides down the plane against a force of magnitude $\frac { 1 } { 2 } m x ^ { 2 }$ newtons acting towards $O$, where $x$ metres is the distance of $P$ from $O$.\\
(a) Find the speed of $P$ when $x = 3$\\
(b) Find the distance $P$ has moved when it first comes to instantaneous rest.\\
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2017 Q3 [9]}}