The authors examined the origins of linear and logarithmic speed-accuracy trade-offs from a dynamic systems perspective on motor control. In each experiment, participants performed 2 reciprocal aiming tasks: (a) a velocity-constrained task in which movement time was imposed and accuracy had to be maximized, and (b) a distance-constrained task in which accuracy was imposed and movement time had to be minimized. In Experiment 1, accuracy was constant across the 2 tasks; in Experiment 2, movement time was kept constant. Behavior in both tasks could be modeled with a single nonlinear equation of motion. Model coefficients captured the particulars of each task, especially apparent for the slowest or most difficult conditions. The distance-constrained task revealed a strong contribution of nonlinear stiffness with a moderate degree of nonlinear damping, favoring local control of speed. The velocity-constrained task revealed weaker nonlinear stiffness with stronger nonlinear damping, favoring global stabilization of the movement with a more constant rate of phase progression. In this way, the different speed-accuracy trade-offs emerged from the task-specific parameterization of the underlying dynamics. (Contains 7 footnotes and 6 figures.)