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This paper studies an assigned-time velocity-planning problem for robotic systems that are subject to velocity and acceleration constraints. The planning problem, which is justified by several robotic applications, poses feasibility issues that are investigated in this paper. In particular, this paper shows that feasible solutions exist if and only if proper interpolating conditions are assigned, and proposes an efficient planning strategy, that is suitable for online implementations. Available degrees of freedom are used to smooth the velocity function by minimizing its maximum jerk.