Brownian motion of particles impacts many branches of
science. We report on the Brownian motion of micronsized
beads of glass held in air in an optical tweezer, over
a wide range of pressures, and measure the instantaneous
velocity of a Brownian particle. Our results provide direct
verification of the energy equipartition theorem for a
Brownian particle. For short times, the ballistic regime of
Brownian motion is observed, in contrast to the usual
diffusive regime. We discuss the applications of these
methods towards cooling the center of mass motion of a
bead in vacuum to the quantum ground motional state.