This article concentrates on the practical prescribed-time leader-following consensus problem of second-order multi-agent systems (MASs) under disconnected time-varying topologies. Firstly, a new practical prescribed-time stability criterion is presented, where the time-varying scaling function is related to connected moments and the derivative inequality is increasing in the disconnected intervals. Secondly, inspired by the backstepping design framework, the practical prescribed-time control protocol is designed, including the distributed velocity estimator, virtual velocity and dynamic event-triggered controller. Thirdly, some consensus conditions for achieving leader-following consensus are established and the Zeno behavior is excluded. Finally, simulation results on unmanned aerial vehicle (UAV) formation tracking are provided to demonstrate the effectiveness of the proposed method.