In this paper, first of all we have given the relations between the absolute, relative and sliding velocities and the relation between the sliding and instantaneous rotations for one parameter Lorentzian motion in 3-dimensional Lorentzian space. In addition to that we have also given the relations between absolute, relative, Coriolis and sliding accelerations of the motion. We have also noted the relations between Coriolis acceleration, instantaneous rotation axis and relative velocity of the motion. Lastly, we have investigated the acceleration centres when $\left\| {\overrightarrow w \wedge \mathop {\overrightarrow w }\limits^ \bullet } \right\|^2\ne0$ and the acceleration axis when $\left\| {\overrightarrow w \wedge \mathop {\overrightarrow w }\limits^ \bullet } \right\|^2 = 0$, where the vector $\vec w$ is the instantaneous rotation axis of the motion. Furthermore, we have given theorems related to these cases.