Proper time of an accelerating particle

[alienslag]

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).

Not sure how to approach this problem. Any help would be greatly appreciated.

 

[Fredrik]

You have to figure out what the world line looks like. You know that $d^2x/dt^2=a$, where a is a constant and you can integrate that equation to find x as a function of t.

If by any chance you meant "constant proper acceleration" when you said "constant acceleration", it's more difficult to figure out what the world line looks like, but DrGreg derived it here, starting with post #13 and ending with a correction in post #28.

 

[alienslag]

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.

 

[Fredrik]

Do you know the definition of proper time? When you write it down, it's clear that you need to know the velocity as a function of time. (Position as a function of time is actually less useful). So what you need to do now is to find out the values of the constants in the equation you found. The boundary conditions that you stated in post #1 contain the information you need for that. The values of the constants depend on where you choose to put the origin of your coordinate system, so try to make a choice that simplifies the math as much as possible.