| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Variable Force |
| Type | Air resistance with other powers |
| Difficulty | Standard +0.8 This M2 question requires setting up and solving a differential equation with a non-standard fractional power (v^(1/3)) for resistance, then manipulating the result to match a given form with fractional exponents. While the method is standard (F=ma, separate variables, integrate), the algebraic manipulation with fractional powers is more demanding than typical M2 resistance problems which usually use v or v^2. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y)6.06a Variable force: dv/dt or v*dv/dx methods |
5 A particle, of mass 12 kg , is moving along a straight horizontal line. At time $t$ seconds, the particle has speed $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$. As the particle moves, it experiences a resistance force of magnitude $4 v ^ { \frac { 1 } { 3 } }$. No other horizontal force acts on the particle.
The initial speed of the particle is $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Show that
$$v = \left( 4 - \frac { 2 } { 9 } t \right) ^ { \frac { 3 } { 2 } }$$
\item Find the value of $t$ when the particle comes to rest.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2013 Q5 [7]}}