| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2006 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Air resistance kv - horizontal motion |
| Difficulty | Standard +0.3 This is a standard M2 resistance-proportional-to-v question with routine setup and integration. Part (a)-(b) test understanding of modelling assumptions (straightforward). Part (c) requires F=ma to get dv/dt = -v/4, then separating variables and integrating—all textbook procedures with no novel insight required. Slightly easier than average due to clean numbers and standard structure. |
| Spec | 6.06a Variable force: dv/dt or v*dv/dx methods |
6 A student is modelling the motion of a small boat as it moves on a lake. When the speed of the boat is $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, the engine is switched off. At time $t$ seconds later, it has a velocity of $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and experiences a resistance force of magnitude $20 v$ newtons. The mass of the boat is 80 kg .
To set up a simple model for the motion of the boat, the student assumes that the water in the lake is still and that the boat travels in a straight line.
\begin{enumerate}[label=(\alph*)]
\item Explain how these two assumptions allow the student to create a simple model.
\item State one other assumption that the student should make.
\item \begin{enumerate}[label=(\roman*)]
\item Express $\frac { \mathrm { d } v } { \mathrm {~d} t }$ in terms of $v$.
\item Find an expression for $v$ in terms of $t$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA M2 2006 Q6 [10]}}