  We propose an action for a free particle in Horava-Lifshitz gravity based on
Foliation Preserving Diffeomorphisms. The action reduces to the usual
relativistic action in the low energy limit and allows for subluminal and
superluminal motions with upper and lower bounds on velocity respectively. We
find that deviation from general relativity is governed by a position dependent
coupling constant which also depends on the mass of the particle. As a result,
light-like geodesics are not affected whereas massive particles follow
geodesics that become mass dependent and hence the equivalence principle is
violated. We make an exact study for geodesics in flat space and a qualitative
analysis for those in a spherically symmetric curved background.
