1. The problem statement, all variables and given/known data A particle of mass m has a position along the x-axis as a function of time given by the equation u = cgt / (1 + g2t2)1/2 where g is a constant and c is the speed of light. (a) Find the 4-velocity of the particle. (b) Express x and t as a function of the proper time of the particle. (c) Find the 4-force acting on the particle. Does it ever exceed the speed of light? 2. Relevant equations uμ = γ(c, u) λ = dt / dτ 3. The attempt at a solution a) Given the first equation, the four-velocity is simply uμ = γ(c, cgt / (1 + g2t2)1/2 I think. b) To find the position, we take the integral of dx/dt and find x = (c/g)(1 + g2t2)1/2 If we let dt = γdτ, then we can easily see t = γτ. However, this is a problem, as the particle is accelerating (its second time derivative is not zero) and that means γ must change. And, another problem, is that we cannot sub in γ = (1 - u2/c2)-1/2 because then we have a recursive definition. c) I know that the four-force is simply mass x second derivative of the four position (or mass x derivative of four-velocity), but I am not too sure how to differentiate it. I also know that the four-force is (F0, F) but I don't know how to find F0 :( PLEASE BE GENTLE. I am a first-year physics student, and my university decided to put general relativity into a first-year course.