Determine the relativistic uniformly accelerated motion, i.e. the rectilinear motion for which the acceleration w in the proper reference frame (at each instant of time) remains constant.
The relativistically invariant condition for uniform acceleration must be expressed by the constancy of the four-scalar which coincides with w2 in the proper reference frame:
wiwi=const≡−c4w2.
Find the velocity v(t) and position x(t) given v=0 and x=0 at t=0, and find the proper time as a function of t.