  Although a plethora of techniques are now available for controlling the group
velocity of an optical wave packet, there are very few options for creating
accelerating or decelerating wave packets whose group velocity varies
controllably along the propagation axis. Here we show that `space-time' wave
packets in which each wavelength is associated with a prescribed spatial
bandwidth enable the realization of optical acceleration and deceleration in
free space. Endowing the field with precise spatio-temporal structure leads to
group-velocity changes as high as $\sim c$ observed over a distance of $\sim20$
mm in free space, which represents a boost of at least $\sim4$ orders of
magnitude over X-waves and Airy pulses. The acceleration implemented is in
principle independent of the initial group velocity, and we have verified this
effect in both the subluminal and superluminal regimes.
