| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2011 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Variable Force |
| Type | Air resistance with other powers |
| Difficulty | Standard +0.3 This is a standard M2 variable force question requiring Newton's second law followed by separating variables and integrating. The fractional power (5/4) makes the algebra slightly less routine than integer powers, but the method is entirely standard for this topic with clear signposting ('show that') at each stage. |
| Spec | 6.06a Variable force: dv/dt or v*dv/dx methods |
6 A car, of mass $m \mathrm {~kg}$, is moving along a straight horizontal road. At time $t$ seconds, the car has speed $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$. As the car moves, it experiences a resistance force of magnitude $2 m v ^ { \frac { 5 } { 4 } }$ newtons. No other horizontal force acts on the car.
\begin{enumerate}[label=(\alph*)]
\item Show that
$$\frac { \mathrm { d } v } { \mathrm {~d} t } = - 2 v ^ { \frac { 5 } { 4 } }$$
(1 mark)
\item The initial speed of the car is $16 \mathrm {~ms} ^ { - 1 }$.
Show that
$$v = \left( \frac { 2 } { t + 1 } \right) ^ { 4 }$$
(5 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2011 Q6 [6]}}