7 Particles \(P\) and \(Q\) leave a fixed point \(A\) at the same time and travel in the same straight line. The velocity of \(P\) after \(t\) seconds is \(6 t ( t - 3 ) \mathrm { m } \mathrm { s } ^ { - 1 }\) and the velocity of \(Q\) after \(t\) seconds is \(( 10 - 2 t ) \mathrm { m } \mathrm { s } ^ { - 1 }\).

1. Sketch, on the same axes, velocity-time graphs for \(P\) and \(Q\) for \(0 \leqslant t \leqslant 5\).
2. Verify that \(P\) and \(Q\) meet after 5 seconds.
3. Find the greatest distance between \(P\) and \(Q\) for \(0 \leqslant t \leqslant 5\).
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