what is the formula for the acceleration felt by an accelerating object? I've spent days googling and cant get a straight answer. some say its the derivative of proper velocity with respect to proper time but others say its the derivative of proper velocity with respect to coordinate time. its obviously the instantaneous acceleration of an object as perceived by an second object traveling at contant velocity equal to the velocity of the first object at that instantaneous moment. I've tried drawing a spacetime diagram and solving equations of lines and doing coordinate transformations but my formulas are a mess of 1/v's and vdeltav's and garbage that doesnt simplify to alpha=a*gamma^3 that I read about.