| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2017 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Air resistance kv² - horizontal motion or engine power |
| Difficulty | Challenging +1.2 This is a standard M4 variable force question with air resistance proportional to v². It requires setting up F=ma with resistance term, separating variables, and integrating—techniques that are routine for this module. The algebra is straightforward (leading to standard forms like tanh or ln), and both parts follow predictable M4 patterns. While it requires multiple steps and careful manipulation, it demands no novel insight beyond applying the standard M4 toolkit. |
| Spec | 6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product6.06a Variable force: dv/dt or v*dv/dx methods |
3. A cyclist and her bicycle have a combined mass of 75 kg . The cyclist travels along a straight horizontal road. The cyclist produces a constant driving force of magnitude 150 N . At time $t$ seconds, the speed of the cyclist is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$, where $v < \sqrt { 50 }$. As the cyclist moves, the total resistance to motion of the cyclist and her bicycle has magnitude $3 v ^ { 2 }$ newtons. The cyclist starts from rest. At time $t$ seconds, she has travelled a distance $x$ metres from her starting point.
Find
\begin{enumerate}[label=(\alph*)]
\item $v$ in terms of $x$,
\item $t$ in terms of $v$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2017 Q3 [12]}}