| Exam Board | SPS |
|---|---|
| Module | SPS ASFM Mechanics (SPS ASFM Mechanics) |
| Year | 2021 |
| Session | May |
| Marks | 10 |
| Topic | Power and driving force |
| Difficulty | Standard +0.3 This is a standard A-level mechanics problem involving power, resistance, and Newton's second law. It requires setting up two simultaneous equations using F=ma and P=Fv at two different speeds, then solving for k and P. Part (ii) uses the standard maximum speed condition (acceleration = 0). While it involves multiple steps and algebraic manipulation, the approach is methodical and follows well-established techniques taught in mechanics modules, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product |
A car of mass $1250$ kg experiences a resistance to its motion of magnitude $kv^2$ N, where $k$ is a constant and $v$ m s$^{-1}$ is the car's speed. The car travels in a straight line along a horizontal road with its engine working at a constant rate of $P$ W. At a point $A$ on the road the car's speed is $15$ m s$^{-1}$ and it has an acceleration of magnitude $0.54$ m s$^{-2}$. At a point $B$ on the road the car's speed is $20$ m s$^{-1}$ and it has an acceleration of magnitude $0.3$ m s$^{-2}$.
\begin{enumerate}[label=(\roman*)]
\item Find the values of $k$ and $P$. [7]
\end{enumerate}
The power is increased to $15$ kW.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Calculate the maximum steady speed of the car on a straight horizontal road. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS ASFM Mechanics 2021 Q5 [10]}}