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\includegraphics[max width=\textwidth, alt={}, center]{31b0d5b6-1593-489b-bbcd-486e7c96ff18-08_451_1340_251_244} A train consists of an engine \(A\) of mass 50000 kg and a carriage \(B\) of mass 20000 kg . The engine and carriage are connected by a rigid coupling. The coupling is modelled as light and horizontal. The resistances to motion acting on \(A\) and \(B\) are 9000 N and 1250 N respectively (see diagram).
The train passes through station \(P\) with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and moves along a straight horizontal track with constant acceleration \(0.01 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) towards station \(Q\). The distance between \(P\) and \(Q\) is 12.95 km .

1. Determine the time, in minutes, to travel between \(P\) and \(Q\). For the train's motion between \(P\) and \(Q\), determine the following.
2. The driving force of the engine.
3. The tension in the coupling between \(A\) and \(B\).