An example of high-speed constant proper-acceleration of an object that began with a (fixed) coordinate-speed perpendicular to the proper-acceleration direction. By defining a plane in (3+1)D containing the proper-acceleration and any fixed-transverse coordinate-speed, one can use this (2+1)D plot to describe constant accelerations in (3+1)D spacetime as well. In the lower-left and upper-right panels, which represent two views of the same motion, velocity and acceleration vectors are drawn at tenth-of-a-year intervals from both Galilean-kinematic (t,"v","a" on left) and traveler-kinematic ("τ","w","α" on right) points of view. The rate of velocity-change vectors (indigo & magenta) are scaled to the same corresponding interval. The upper-left panel represents low-speed motion in which the Galilean and traveler kinematics show the same thing. The lower-right panel shows how the traveler-kinematic changes shape further as one moves into the hyper-relativistic regime.