$$a^\mu=\frac{d^2 x^\mu}{d au^2}=\frac{d}{d au}\frac{dx^\mu}{d au}=\frac{d}{d au}v^\mu=0$$ (the upper index $\mu$ is just there to indicate the position and other vectors have four components, three corresponding to space and one to time: $t,x,y,z$ in cartesian coordinates.