| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2012 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Differential equations |
| Type | Particle motion - velocity/time (dv/dt = f(v,t)) |
| Difficulty | Standard +0.3 This is a standard M2 differential equations question involving Newton's second law with resistance. Part (a) requires straightforward application of F=ma with given forces (2 marks suggests routine setup). Part (b) involves separating variables and integrating a simple linear DE—both are textbook exercises requiring method recall rather than problem-solving insight. Slightly above average difficulty due to the mechanics context and DE solving, but well within standard M2 scope. |
| Spec | 6.06a Variable force: dv/dt or v*dv/dx methods |
7 A stone, of mass 5 kg , is projected vertically downwards, in a viscous liquid, with an initial speed of $7 \mathrm {~ms} ^ { - 1 }$.
At time $t$ seconds after it is projected, the stone has speed $v \mathrm {~ms} ^ { - 1 }$ and it experiences a resistance force of magnitude $9.8 v$ newtons.
\begin{enumerate}[label=(\alph*)]
\item When $t \geqslant 0$, show that
$$\frac { \mathrm { d } v } { \mathrm {~d} t } = - 1.96 ( v - 5 )$$
(2 marks)
\item Find $v$ in terms of $t$.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2012 Q7 [7]}}