| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Session | Specimen |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Air resistance kv² - projected vertically upward |
| Difficulty | Challenging +1.2 This is a standard M4 differential equations problem involving air resistance proportional to v². While it requires setting up F=ma with resistance, separating variables, and integrating (multiple steps over 9 marks), the technique is a core M4 skill practiced extensively. The choice of initial speed √(g/k) simplifies the algebra considerably, making this a textbook-style question rather than one requiring novel insight. |
| Spec | 6.06a Variable force: dv/dt or v*dv/dx methods |
A ball of mass $m$ is thrown vertically upwards from the ground. When its speed is $v$ the magnitude of the air resistance is modelled as being $mkv^2$, where $k$ is a positive constant. The ball is projected with speed $\sqrt{\frac{g}{k}}$.
By modelling the ball as a particle,
\begin{enumerate}[label=(\alph*)]
\item find the greatest height reached by the ball.
[9]
\item State one physical factor which is ignored in this model.
[1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 Q3 [10]}}