| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2013 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Air resistance kv - vertical motion |
| Difficulty | Standard +0.8 This is a standard M4 resisting forces question requiring formation and solution of a differential equation (Newton's second law with air resistance), followed by integration to find distance. While it involves multiple steps and exponential functions, it follows a well-established method taught explicitly in M4. The 8+5 mark allocation and 'show that' format indicate moderate difficulty, but this is routine for Further Maths mechanics students who have practiced this exact type of problem. |
| Spec | 1.08d Evaluate definite integrals: between limits3.03r Friction: concept and vector form6.06a Variable force: dv/dt or v*dv/dx methods |
A particle $P$ of mass $0.5$ kg falls vertically from rest. After $t$ seconds it has speed $v$ m s$^{-1}$. A resisting force of magnitude $1.5v$ newtons acts on $P$ as it falls.
\begin{enumerate}[label=(\alph*)]
\item Show that $3v = 9.8(1 - e^{-3t})$.
[8]
\item Find the distance that $P$ falls in the first two seconds of its motion.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2013 Q1 [13]}}