| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2002 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Motion with exponential force |
| Difficulty | Standard +0.3 This is a standard M3 variable force question requiring application of F=ma with v dv/dx, followed by integration of an exponential function and interpretation of a limiting value. The techniques are routine for this module, though the exponential makes it slightly above average difficulty compared to simpler polynomial force questions. |
| Spec | 3.02f Non-uniform acceleration: using differentiation and integration3.03d Newton's second law: 2D vectors6.06a Variable force: dv/dt or v*dv/dx methods |
A particle $P$ of mass 2.5 kg moves along the positive $x$-axis. It moves away from a fixed origin $O$, under the action of a force directed away from $O$. When $OP = x$ metres the magnitude of the force is $2e^{-0.1x}$ newtons and the speed of $P$ is $v$ m s$^{-1}$. When $x = 0$, $v = 2$. Find
\begin{enumerate}[label=(\alph*)]
\item $v^2$ in terms of $x$,
[6]
\item the value of $x$ when $v = 4$.
[3]
\item Give a reason why the speed of $P$ does not exceed $\sqrt{20}$ m s$^{-1}$.
[1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2002 Q3 [10]}}