Question: consider a particle moving along the xaxis whose velocity as...
Consider a particle moving along the x-axis whose velocity as a function of time is , where g is a constant. Compute the acceleration in a frame in which the particle is instantaneously at rest. You should find that the result is independent of time. Hence, this motion is often referred to as uniform proper acceleration. It is the most natural definition of "uniform acceleration" in special relativity.
Note: When I gave this problem a try, I differentiated the above equation to get acceleration and got an equation in terms of t. I believe I should then substitute the proper time "tau" (which is the same in all frames) in the equation. However, I am not sure this is the correct approach. Please explain reasoning with your steps. It will be greatly appreciated. Thank you :)