What is the distance x in terms of kinetic energy, using relativistic mechanics?

[Yura]

its a four part question but the first part has me stuck:

the question:
A particle of mass m is accelerated from rest by a constant force F along a straight line for a duration of time t. Use relativistic mechanics unless explicitly stated otherwise. Also remember that the definitions of work and impulse are unchanged by special relativity.
(a) What are the kinetic and total energies of the particle as functions of the particle’s position? Give some justification for your answer.

so i need the distance (which i am going to label "x") in terms of the kinetic energy

is there an relativistic equation or formula withe "x" already as a function of the kinetic energy?
or is there a way to do this, given there is a formula for the velocity in relativity suing einsteins theory by somehow putting the velocity as a function of the distance relativistically and subbing it in?

im not sure how to go at this one at all, i will have another try, but it would help if there was such a formula

 

[Meir Achuz]

F is ambiguous in SR. I will assume F=dp/dt is meant.
Use dE/dt=vF=(dE/dx)(dx/dt)=v(dE/dx) to get F=dE/dx.
This happens to be the same as the NR result.
E is the total energy with E^2=p^2+m^2.

 

[jtbell]

is there an relativistic equation or formula withe "x" already as a function of the kinetic energy?

Just as in classical mechanics, for a constant force applied in the direction of motion, W = Fx (work equals force times distance). Since the object starts from rest, its kinetic energy equals the work done on it (work-energy theorem).