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1) Is it right to use v=[tex]\sqrt{2aD}[/tex] to find the find velocity, and D=1/2at[tex]^{2}[/tex]. to find final velocity and time elapsed relative to the rest frame. I'm fairly sure this is correct.

2) what is the final speed(v'), time elapsed(t'), acceleration(a') & distance(D') relative the moving reference frame.

I'd be very happy you someone show a derivation as well. Thanks