Question

1a.) Let us first ask what we mean by "uniform acceleration." After all, a rocket approaching the speed of light c can't change its velocity at a uniform rate forever without exceeding c at some point. Go into the frame moving instantaneously at velocity v with the rocket relative to the "lab." The instantancous rocket velocity, v, vanishes in this frame. Wait a time dt later, as measured in this frame. The rocket now has velocity do' in this same frame. What we mean by constant acceleration is du,/It' a, is constant. The acceleration measured in the lab is certainly not constant! The question is, how is the lab acceleration a = dv/dt related to the constant a'? To answer this, let V1-, the spatial part of the 4-vector Va associated with ordinary velocity v. The same relation holds for Vi and u. Assume for the moment that the primed and unprimed frames differ by some arbitrary velocity w. The 4-veloci differentials are given by: the where Vo 1/V1-2. Explain.

Answer 1

a' would be instantaneous acceleration. If we take the average of a' at different instants, we would get a.

I-Vi I-V2 ーレ2 2

So this will be same as given expression when the two terms in the curly brackets can be neglected.