# Relativistic and not relativistic motions

by bernhard.rothenstein
Tags: motions, relativistic
 Emeritus Sci Advisor P: 7,596 Alternately, given any function v(t) < c, one can compute the acceleration required to cause the specified motion. The only thing "special" about special relativistic motion is that |v(t)| < 1. One can also show that the rate of change of momentum with respect to time becomes infinite as v->c, i.e. $$\frac{dp}{dt} = \frac{dp}{dv} \frac{dv}{dt} = \frac{m}{{\left( 1 - \frac{v^2}{c^2} \right)} ^ \frac{3}{2}} \frac{dv} {dt}$$ Thus as v->c, dp/dt becomes infinite. One does not really need dynamics to see this, the fact is that if one adds together any number of velocities less than 'c' using the SR velocity addition formula, one gets a resultant velocity less than 'c'. The process of accelerating is just a process of "adding to" one's original velocity. One must use the SR form of the velocity additon law. Delta-v = a * delta t is true only in the objects rest frame, the SR velocity additon formula converts the delta-v in the objects rest frame into the delta-v in the coordinate frame.