| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2006 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Air resistance kv - vertical motion |
| Difficulty | Standard +0.3 This is a standard M4 resisted motion question requiring Newton's second law setup and solving a first-order linear ODE with separable variables. Part (a) is routine force equation manipulation (2 marks), while part (b) involves standard integration and applying initial conditions. The techniques are well-practiced in M4 with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y)6.06a Variable force: dv/dt or v*dv/dx methods |
A particle $P$ of mass $0.5$ kg is released from rest at time $t = 0$ and falls vertically through a liquid. The motion of $P$ is resisted by a force of magnitude $2v$ N, where $v$ m s$^{-1}$ is the speed of $v$ at time $t$ seconds.
\begin{enumerate}[label=(\alph*)]
\item Show that $5 \frac{\mathrm{d}v}{\mathrm{d}t} = 49 - 20v$.
[2]
\item Find the speed of $P$ when $t = 1$.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2006 Q1 [7]}}