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\includegraphics[max width=\textwidth, alt={}, center]{99d30766-9c1b-43a8-986a-112b78b08146-4_634_1127_934_507} A car \(P\) starts from rest and travels along a straight road for 600 s . The \(( t , v )\) graph for the journey is shown in the diagram. This graph consists of three straight line segments. Find

1. the distance travelled by \(P\),
2. the deceleration of \(P\) during the interval \(500 < t < 600\). Another car \(Q\) starts from rest at the same instant as \(P\) and travels in the same direction along the same road for 600 s . At time \(t \mathrm {~s}\) after starting the velocity of \(Q\) is \(\left( 600 t ^ { 2 } - t ^ { 3 } \right) \times 10 ^ { - 6 } \mathrm {~ms} ^ { - 1 }\).
3. Find an expression in terms of \(t\) for the acceleration of \(Q\).
4. Find how much less \(Q\) 's deceleration is than \(P\) 's when \(t = 550\).
5. Show that \(Q\) has its maximum velocity when \(t = 400\).
6. Find how much further \(Q\) has travelled than \(P\) when \(t = 400\).