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Say I am already travelling at velocity "v" where "v" is approaching the speed of light. I then, over a period of observer time "t", accelerate at a constant rate of "a". How do I then calculate the distance "d" I travelled over the period of time "t" (since I started accelerating)? Also how do I calculate my subjective time "T" that elapsed over time "t"?

I understand that if my velocity remains constant then:

T = t * √(1 - (v

^{2}/ c

^{2}))

but how does the acceleration affect my subjective time? I found another equation:

T = (c / a) * arsinh(at / c)

Can I simply add them together? I would assume not due to special relativity. How do I combine the formulas?

I also understand that if I were accelerating without any existing velocity:

d = (c

^{2}/ a) * (√(1 + (at / c)

^{2}) - 1)

but shouldn't my existing velocity be taken into consideration when calculating the distance that I cover? I don't see "v" anywhere in that equation. How to I add it?

Also can I just make "a" negative and run it through the formulas again afterwards to decelerate?