Given an ideal rocket in a friction-free, gravity-free environment: A precise amount of energy E is applied to accelerating a rocket. An external observer at the origin (rocket velocity=0) watches the rocket accelerate to a final velocity V. As expected, the origin observer finds that V precisely matches the value required for E to equal the kinetic energy (KE) of the rocket. An observer aboard the rocket only has an accelerometer and a proper clock. If the rocket observer integrates his accelerometer readings using the proper clock during the acceleration event to find his final velocity V', will V = V'? Thanks!