  We demonstrate time-of-flight measurements for an ultracold levitated
nanoparticle and reveal its velocity for the translational motion brought to
the quantum ground state. We discover that the velocity distributions obtained
with repeated release-and-recapture measurements are significantly broadened
via librational motions of the nanoparticle. Under feedback cooling on all the
librational motions, we recover the velocity distributions in reasonable
agreement with an expectation from the occupation number, with approximately
twice the width of the quantum limit. The strong impact of librational motions
on the translational motions is understood as a result of the deviation between
the libration center and the center of mass, induced by the asymmetry of the
nanoparticle. Our results elucidate the importance of the control over
librational motions and establish the basis for exploring quantum mechanical
properties of levitated nanoparticles in terms of their velocity.
