  Velocity effects in first-order Schwarzschild deflection of light and
particles have been explored in the previous literature. In this paper, we
investigate the roto-translational-motion induced deflection by one moving Kerr
black hole with an arbitrary but constant speed. It is shown that the coupling
between the effects of the rotation and the translational motion always exists
for both light and particles. The contribution of the roto-translational
deflection to the total bending angle is discussed in detail. This ratio takes
upper limit for light and it decreases monotonically with increasing
translational velocity for a massive particle. For a given translational
velocity of black hole, this ratio increases with the particle' velocity. In
addition, the Post-Newtonian dynamics of the photon and particle is also
presented.
