A particle \(P\) is moving along a straight line with acceleration \(3 k u-k v\) where \(v\) is its velocity at time \(t\), \(u\) is its initial velocity and \(k\) is a constant. The velocity and acceleration of \(P\) are both in the direction of increasing displacement from the initial position.
(a) Find the time taken for \(P\) to achieve a velocity of \(2 u\).
(b) Find an expression for the displacement of \(P\) from its initial position when its velocity is \(2 u\).