| Exam Board | SPS |
|---|---|
| Module | SPS FM Mechanics (SPS FM Mechanics) |
| Year | 2026 |
| Session | January |
| Marks | 8 |
| Topic | Power and driving force |
| Type | Instantaneous change in power or force |
| Difficulty | Standard +0.3 This is a standard Further Maths mechanics question on power, forces on an incline, and Newton's second law. Part (a) uses P=Fv at constant speed (equilibrium), part (b) applies F=ma with changed power. The calculations are straightforward with no conceptual surprises, making it slightly easier than average A-level standard. |
| Spec | 6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product |
A van of mass 600 kg is moving up a straight road inclined at an angle $\theta$ to the horizontal, where $\sin \theta = \frac{1}{16}$. The resistance to motion of the van from non-gravitational forces has constant magnitude $R$ newtons. When the van is moving at a constant speed of 20 m s$^{-1}$, the van's engine is working at a constant rate of 25 kW.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $R$. [4]
\end{enumerate}
The power developed by the van's engine is now increased to 30 kW. The resistance to motion from non-gravitational forces is unchanged. At the instant when the van is moving up the road at 20 m s$^{-1}$, the acceleration of the van is $a$ m s$^{-2}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the value of $a$. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Mechanics 2026 Q1 [8]}}