This paper addresses the issue of motion planning in dynamic environments using Velocity Obstacles. Specifically, we propose an adaptive time horizon to truncate the velocity obstacle so that its boundary closely, yet conservatively, approximates the boundary of the set of states from which collision is unavoidable. We wish to develop a representation such that any velocity vector that does not penetrate the velocity obstacle is safe, i.e. an avoidance maneuver exists, and any that does is not. Such clear partitioning between safe and unsafe velocities would allow safe planning with only one step look ahead, and can produce faster trajectories than the conservative trajectories produced when using an infinite time horizon. The computation of the adaptive time horizon is formulated as a minimum time problem, which is solved numerically for each static or moving obstacle. It is used in an on-line planner that generates locally time optimal trajectories to the goal. The planner is demonstrated for static and moving obstacles, and for on-line motion planning in a crowded dynamic environment.