# Two objects undergoing proper acceleration

Is there an inertial frame ($$x'$$, $$t'$$) in which two objects undergoing proper acceleration in the positive x-direction (e.g. starting from rest at $$t=0$$ from $$x=0$$ and $$x=L$$) where the two objects end up at rest?

In this frame, where and when did each object begin moving and how far apart do they end up? I know that in the stationary frame the two objects are always a distance $$L$$ apart. How far apart are they from the perspective of the objects themselves?