Precise control over the translational motion of atoms and molecules is important for a large range of scientific and industrial processes. Applications range from surface growth and deposition to elucidating the details of chemical reactions through controlled collisions. The critical challenge faced by many experiments is the production of a beam of particles with a narrow velocity spread, a precisely controlled mean velocity, and sufficient flux over a wide range. We demonstrate this fine control of velocity using strong optical fields that trap and accelerate particles up to velocities of hundreds of metres per second. This acceleration occurs over tens of nanoseconds and on micrometre length scales. Particle velocity can be continuously tuned over a wide range while maintaining a narrow velocity spread. Our method is very general and will allow acceleration or deceleration of a wide variety of neutral atomic and molecular species, as well as nanoscale particles.