6 A particle moves in a straight line. It starts from rest from a fixed point \(O\) on the line. Its velocity at time \(t \mathrm {~s}\) after leaving \(O\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where \(v = t ^ { 2 } - 8 t ^ { \frac { 3 } { 2 } } + 10 t\).

1. Find the displacement of the particle from \(O\) when \(t = 1\).
2. Show that the minimum velocity of the particle is \(- 125 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).