Feedback control systems and many manufacturing processes can benefit from precise velocity information, although direct measurement of linear velocity is often impractical and/or costly. The accepted procedure of inferring velocity from quantized position measurements can in some instances yield noisy and inaccurate estimates. This paper proposes an optimal velocity estimation scheme incorporating measured acceleration data for use in slowly moving systems. Simulation and experimental results demonstrate improved low speed velocity estimation compared to traditional methods. The optimal velocity feedback is also shown to decrease overshoot in a closed-loop implementation.