| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Variable Force |
| Type | Air resistance kv - horizontal motion |
| Difficulty | Standard +0.3 This is a standard M2 differential equations question with resistance proportional to v. Part (a) requires straightforward application of F=ma with given forces, and part (b) involves separating variables and integrating—a routine technique at this level. The algebra is clean and the method is textbook-standard, making it slightly easier than average. |
| Spec | 1.07t Construct differential equations: in context1.08k Separable differential equations: dy/dx = f(x)g(y)6.06a Variable force: dv/dt or v*dv/dx methods |
6 A car accelerates from rest along a straight horizontal road.
The car's engine produces a constant horizontal force of magnitude 4000 N .\\
At time $t$ seconds, the speed of the car is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$, and a resistance force of magnitude $40 v$ newtons acts upon the car.
The mass of the car is 1600 kg .
\begin{enumerate}[label=(\alph*)]
\item Show that $\frac { \mathrm { d } v } { \mathrm {~d} t } = \frac { 100 - v } { 40 }$.
\item Find the velocity of the car at time $t$.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2013 Q6 [8]}}