  The kinematics of particles moving in rainbow spacetime is studied in this
paper. In particular the geodesics of a massive particle in rainbow flat
spacetime is obtained when the semi-classical effect of its own energy on the
background is taken into account. We show that in general the trajectory of a
freely falling particle remains unchanged which is still a straight line as in
the flat spacetime. The implication to the Unruh effect in rainbow flat
spacetime is also discussed.
