<p>The flying focus features an intensity peak that propagates at a focal velocity that is decoupled from the group velocity of the medium. Control over the velocity of the focal point is predicted to revolutionize secondary source experiments by allowing velocity matching of physical processes at the core of nonlinear optics and high-field physics. Despite this promise, experimental demonstrations have lagged pioneering theoretical work due to the difficulty of creating an ultrashort flying focus in the laboratory. In this article, the spatiotemporal shaping of a terahertz pulse generated via gas-phase photoionization by a two-color, ultrashort flying focus is described. The combination of radial group delay provided by reflective, radially-stepped echelons and spherical aberration produced by an axiparabola generates a flying focus with sub- and superluminal focal point velocities. The flying focus efficiently generates terahertz radiation that exhibits fundamentally different spatiotemporal properties based on its velocity. We present detailed measurements of the spatial and temporal properties of the terahertz radiation and measure its focal velocity. This demonstration shows the utility of terahertz generation with a flying focus and enables future experiments in nonlinear optics with spatiotemporal control.</p>