| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2018 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Given velocity function find force |
| Difficulty | Challenging +1.2 This is a Further Maths M4 question requiring differentiation of an exponential product to find velocity and acceleration, then applying F=ma with two forces. While it involves multiple steps (differentiate twice, substitute into force equation, compare coefficients), the techniques are standard for M4 and the given displacement function makes it methodical rather than requiring problem-solving insight. |
| Spec | 4.10g Damped oscillations: model and interpret6.06a Variable force: dv/dt or v*dv/dx methods |
4. A particle $P$ of mass 0.5 kg moves in a horizontal straight line. At time $t$ seconds $( t \geqslant 0 )$, the displacement of $P$ from a fixed point $O$ of the line is $x$ metres, the speed of $P$ is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $P$ is moving in the direction of $x$ increasing. A force of magnitude $k x$ newtons acts on $P$ in the direction $P O$. The motion of $P$ is also subject to a resistance of magnitude $\lambda v$ newtons.
Given that
$$x = ( 1.5 + 10 t ) \mathrm { e } ^ { - 4 t }$$
find
\begin{enumerate}[label=(\alph*)]
\item the value of $k$ and the value of $\lambda$,
\item the distance from $P$ to $O$ when $P$ is instantaneously at rest.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2018 Q4 [11]}}