I'm sorry, this topic has certainly already been covered, but I didn't find what I need. I'm trying to compute x(t) in an inertial frame if a rocket has a constant acceleration "a" as measured with accelerometers inside of it. I made these (clearly wrong) computations: In a co-moving frame which speed v (with respect the stationary frame) equals the instantaneous speed of the rocket, the rocket is seen to acquire a speed du during the interval of time dt'. The variation of the speed, as seen from the stationary inertial frame is: dv = (v + du)/(1 + v*du/c^2) - v = [1 - (v/c)^2]du The interval of time in the inertial frame is: dt = Sqrt[1 - (v/c)^2]dt' <-- this is the mistake so: dv/dt = [1 - (v/c)^2]du/Sqrt[1 - (v/c)^2]dt' = = Sqrt[1 - (v/c)^2]du/dt' = Sqrt[1 - (v/c)^2]*a Integrating I have v(t) proportional to sin(a*t) which is a clearly wrong result. Can you help me? Thanks.