| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Variable resistance: find k or constants |
| Difficulty | Standard +0.3 This is a standard M2 power-resistance question requiring application of F=ma and P=Fv formulas. Part (i) involves setting up an equation using Newton's second law with the given resistance form, then solving for k. Part (ii) uses the steady speed condition (acceleration = 0) to find maximum power. Both parts follow routine M2 procedures with straightforward algebra and no novel problem-solving insight required, making it slightly easier than average. |
| Spec | 3.02a Kinematics language: position, displacement, velocity, acceleration3.03c Newton's second law: F=ma one dimension6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
A car of mass 1500 kg travels along a straight horizontal road. The resistance to the motion of the car is $kv^{\frac{3}{2}}$ N, where $v$ ms$^{-1}$ is the speed of the car and $k$ is a constant. At the instant when the engine produces a power of 15000 W, the car has speed 15 ms$^{-1}$ and is accelerating at 0.4 ms$^{-2}$.
\begin{enumerate}[label=(\roman*)]
\item Find the value of $k$. [4]
\end{enumerate}
It is given that the greatest steady speed of the car on this road is 30 ms$^{-1}$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the greatest power that the engine can produce. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR M2 2013 Q2 [7]}}