5 A particle starts from a fixed origin with velocity \(0.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and moves in a straight line. The acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\) of the particle \(t \mathrm {~s}\) after it leaves the origin is given by \(a = k \left( 3 t ^ { 2 } - 12 t + 2 \right)\), where \(k\) is a constant. When \(t = 1\), the velocity of \(P\) is \(0.1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Show that the value of \(k\) is 0.1 .
2. Find an expression for the displacement of the particle from the origin in terms of \(t\).
3. Hence verify that the particle is again at the origin at \(t = 2\).