A thin, nonconducting disk of radius \(R\) carries a total positive charge \(Q\) distributed uniformly over its surface. The electric potential along the central axis of the disk as a function of distance \(z\) from the center is given by \(V(z) = \dfrac{2kQ}{R^2} \left(\sqrt{z^2 + R^2} - z\right)\), where \(k\) is the Coulomb constant. A small particle of mass \(m\) and positive charge \(q\) is projected from a point on the axis at distance \(z = R\) directly toward the center of the disk (\(z = 0\)). What is the minimum initial speed \(v_0\) the particle must have at \(z = R\) to reach the center of the disk?