5 A particle starts from rest at a point \(A\) at time \(t = 0\), where \(t\) is in seconds. The particle moves in a straight line. For \(0 \leqslant t \leqslant 4\) the acceleration is \(1.8 t \mathrm {~m} \mathrm {~s} ^ { - 2 }\), and for \(4 \leqslant t \leqslant 7\) the particle has constant acceleration \(7.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).

1. Find an expression for the velocity of the particle in terms of \(t\), valid for \(0 \leqslant t \leqslant 4\).
2. Show that the displacement of the particle from \(A\) is 19.2 m when \(t = 4\).
3. Find the displacement of the particle from \(A\) when \(t = 7\).