I am not sure I follow, could you please elaborate. X as a function of t is 1/2at^2 + vot +xo, but then how would I find the proper time of the particle from this relationship? Also I mean constant acceleration and not proper acceleration.
A particle has a constant acceleration in a laboratory from 0 to 0.5c in 3 seconds. What time elapses for the particle (i.e. what is the proper time for the particle)? Hint: (you will have to integrate the proper time of the particle over the 3 seconds as measured in the laboratory frame)...