This paper presents the first experimental realization of a scheme that allows for the tuning of the velocity of peak intensity of a focal spot with relativistic intensity. By combining a tunable pulse-front curvature with the axial intensity deposition characteristics of an axiparabola, an aspheric optical element, this system provides control over the dynamics of laser-wakefield accelerators. We demonstrate the ability to modify the velocity of peak intensity of ultrashort laser pulses to be superluminal or subluminal. The experimental results are supported by theoretical calculations and simulations, strengthening the case for the axiparabola as a pertinent strategy to achieve more efficient acceleration.