  When introducing special relativity, an elegant connection to familiar rules
governing Galilean constant acceleration can be made, by describing first the
discovery at high speeds that the clocks (as well as odometers) of different
travelers may proceed at different rates. One may then show how to parameterize
any given interval of constant acceleration with {\em either}: Newtonian
(low-velocity approximation) time, inertial relativistic (unaccelerated
observer) time, or traveler proper (accelerated observer) time, by defining
separate velocities for each of these three kinematics as well. Kinematic
invariance remains intact for proper acceleration since $m a_o = dE/dx$. This
approach allows students to solve relativistic constant acceleration problems
{\em with the Newtonian equations}! It also points up the self-contained and
special nature of the accelerated-observer kinematic, with its frame-invariant
time, 4-vector velocities which in traveler terms exceed Newtonian values and
the speed of light, and of course relativistic momentum conservation.
