6 A particle of mass \(m \mathrm {~kg}\) falls vertically under gravity, from rest. At time \(t \mathrm {~s} , P\) has fallen \(x \mathrm {~m}\) and has velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The only forces acting on \(P\) are its weight and a resistance of magnitude \(k m g v \mathrm {~N}\), where \(k\) is a constant.

1. Find an expression for \(v\) in terms of \(t , g\) and \(k\).
2. Given that \(k = 0.05\), find, in metres, how far \(P\) has fallen when its speed is \(12 \mathrm {~ms} ^ { - 1 }\).