A car of mass 1000 kg is moving along a straight horizontal road with a constant acceleration of $j$ m s$^{-2}$. The resistance to motion is modelled as a constant force of magnitude 1200 N. When the car is travelling at 12 m s$^{-1}$, the power generated by the engine of the car is 24 kW.

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\item Calculate the value of $j$.
[4]
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When the car is travelling at 14 m s$^{-1}$, the engine is switched off and the car comes to rest, without braking, in a distance of $d$ metres. Assuming the same model for resistance,

\begin{enumerate}[label=(\alph*)]
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\item use the work-energy principle to calculate the value of $d$.
[3]
\end{enumerate}

\begin{enumerate}[label=(\alph*)]
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\item Give a reason why the model used for the resistance to motion may not be realistic.
[1]
\end{enumerate}

A uniform ladder $AB$, of mass $m$ and length $2a$, has one end $A$ on rough horizontal ground. The other end $B$ rests against a smooth vertical wall. The ladder is in a vertical plane perpendicular to the wall. The ladder makes an angle $α$ with the horizontal, where $\tan α = \frac{4}{3}$. A child of mass $2m$ stands on the ladder at $C$ where $AC = \frac{1}{4}a$, as shown in Fig. 1. The ladder and the child are in equilibrium.

By modelling the ladder as a rod and the child as a particle, calculate the least possible value of the coefficient of friction between the ladder and the ground.
[9]

\hfill \mbox{\textit{Edexcel M2  Q2 [17]}}