4 A particle of mass 0.4 kg , moving on a smooth horizontal surface, passes through a point \(O\) with velocity \(10 \mathrm {~ms} ^ { - 1 }\). At time \(t \mathrm {~s}\) after the particle passes through \(O\), the particle has a displacement \(x \mathrm {~m}\) from \(O\), has a velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) away from \(O\), and is acted on by a force of magnitude \(\frac { 1 } { 8 } v \mathrm {~N}\) acting towards \(O\). Find

1. the time taken for the velocity of the particle to reduce from \(10 \mathrm {~ms} ^ { - 1 }\) to \(5 \mathrm {~ms} ^ { - 1 }\),
2. the average velocity of the particle over this time.