A car has mass 550 kg. When the car travels along a straight horizontal road there is a constant resistance to the motion of magnitude $R$ newtons, the engine of the car is working at a rate of $P$ watts and the car maintains a constant speed of 30 m s$^{-1}$. When the car travels up a line of greatest slope of a hill which is inclined at $\theta$ to the horizontal, where $\sin \theta = \frac{1}{14}$, with the engine working at a rate of $P$ watts, it maintains a constant speed of 25 m s$^{-1}$. The non-gravitational resistance to motion when the car travels up the hill is a constant force of magnitude $R$ newtons.

\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find the value of $R$.
\item Find the value of $P$. [8]
\end{enumerate}
\item Find the acceleration of the car when it travels along the straight horizontal road at 20 m s$^{-1}$ with the engine working at 50 kW. [4]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2014 Q3 [12]}}