# maximum distance between accelerating objects started at different times [closed]

Let there be two objects that have zero relative velocity with respect to each other in an inertial frame. If they both undergo identical accelerations, but one starts the acceleration at t = T1 and the other starts the acceleration at t = T2, then per special relativity the maximum distance that rest frame can measure between the two objects is (T1-T2) * c What acceleration equations show that the separation between these two objects as t approaches infinity approaches c * (T1-T2)

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## closed as too localized by David Z♦Jul 17 '12 at 7:56

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Do you understand that the answer is infinite in Newtonian mechanics and why? Can you express the (time,position) of a uniformly accelerating body from the POV of some fixed reference frame in special relativity? – dmckee Jul 16 '12 at 15:54
Is this a homework problem? We only answer conceptual questions here, we won't do your HW for you. – DJBunk Jul 16 '12 at 16:00
Good grief, it's just a quote of a problem. Is it too much to ask of the OP to at least make the effort to ask for help even if it's just something like "I don't have a clue how to even start this problem, what do I do?" and perhaps give some thanks for any hints or help in advance? – Alfred Centauri Jul 16 '12 at 16:53
It certainly looks like a homework problem, but it's also a very interesting question. I had to dig out my copy of Gravitation (chapter 6) to answer it. If we leave it a few days am I allowed to post the answer here? Alternatively I suppose anyone who's interested in the answer could just re-ask the question in a less contentious way ... – John Rennie Jul 16 '12 at 17:40
The interesting thing is that an intuitive argument can be made that must be far easier than looking up or deriving the acceleration equations. Since both objects undergo identical accelerations, their world lines are congruent; their world lines are displaced in time by the difference in their start times. Since both objects asymptotically approach $c$, their world lines approach null lines, i.e., their spatial separation asymptotically approaches their temporal separation. – Alfred Centauri Jul 16 '12 at 19:01