Figure 2. The position x() as calculated from (5), the velocity β() as given in (7), and the acceleration α() as given in (9), all calculated as functions of time (blue) in the stationary frame (with x0 = 1) in the frozen-time case (3). Note that these curves are mathematically identical to the corresponding curves (red, coinciding) calculated from a different starting point using (10) through (15) with α = 1/x0

From

Can Time in Special Relativity Appear Frozen despite the Clock Hypothesis Says it Cannot?

Arne Bergstrom

International Journal of Physics. 2013, 1(6), 146-150 doi:10.12691/ijp-1-6-3