| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Air resistance kv - vertical motion |
| Difficulty | Standard +0.3 Part (a) is a straightforward application of Newton's second law with two forces (weight and resistance), requiring standard bookwork. Part (b) involves solving a first-order linear differential equation with initial conditions—a standard M2 technique using separation of variables or integrating factor. While it requires careful algebraic manipulation over 6 marks, this is a routine mechanics problem with no novel insight needed, 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 stone, of mass $m$, falls vertically downwards under gravity through still water. At time $t$, the stone has speed $v$ and it experiences a resistance force of magnitude $\lambda mv$, where $\lambda$ is a constant.
\begin{enumerate}[label=(\alph*)]
\item Show that
$$\frac{\text{d}v}{\text{d}t} = g - \lambda v$$
[2 marks]
\item The initial speed of the stone is $u$.
Find an expression for $v$ at time $t$.
[6 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2016 Q6 [8]}}