| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2014 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Variable resistance: find constant speed |
| Difficulty | Standard +0.8 This M4 question requires applying power-force relationships (P=Fv) and solving a differential equation involving variable resistance. Part (a) is straightforward substitution, but part (b) requires setting up and integrating a separable differential equation with v dv/dx form, then evaluating a non-trivial integral—this is standard M4 content but involves multiple sophisticated steps beyond typical A-level mechanics. |
| Spec | 6.02l Power and velocity: P = Fv6.06a Variable force: dv/dt or v*dv/dx methods |
A car of mass 1000 kg is moving along a straight horizontal road. The engine of the car is working at a constant rate of 25 kW. When the speed of the car is $v$ m s$^{-1}$, the resistance to motion has magnitude $10v$ newtons.
\begin{enumerate}[label=(\alph*)]
\item Show that, at the instant when $v = 20$, the acceleration of the car is 1.05 m s$^{-2}$. [3]
\item Find the distance travelled by the car as it accelerates from a speed of 10 m s$^{-1}$ to a speed of 20 m s$^{-1}$. [8]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2014 Q2 [11]}}