A smooth wire has the form of the helix x = a cos θ, y = a sin θ, z = bθ, where θ is a real parameter, and a, b are positive constants. The wire is fixed with the axis Oz pointing vertically upwards.
A particle P, which can slide freely on the wire, is released from rest at the point (a, 0, 2πb). Find the speed of P when it reaches the point (a, 0, 0) and the time taken for it to do so.