6 A particle moves in a straight line \(A B\). The velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) of the particle \(t \mathrm {~s}\) after leaving \(A\) is given by \(v = k \left( t ^ { 2 } - 10 t + 21 \right)\), where \(k\) is a constant. The displacement of the particle from \(A\), in the direction towards \(B\), is 2.85 m when \(t = 3\) and is 2.4 m when \(t = 6\).

1. Find the value of \(k\). Hence find an expression, in terms of \(t\), for the displacement of the particle from \(A\).
2. Find the displacement of the particle from \(A\) when its velocity is a minimum.