A particle \(Q\) of mass \(m \mathrm{~kg}\) falls from rest under gravity. The motion of \(Q\) is resisted by a force of magnitude \(m k v \mathrm{~N}\), where \(v \mathrm{~ms}^{-1}\) is the speed of \(Q\) at time \(t \mathrm{~s}\) and \(k\) is a positive constant.

Find an expression for \(v\) in terms of \(g, k\) and \(t\).