I have just been thinking....
Lets take an object in space and start accelerating it, as we accelerate it the object takes on mass. Now, lets stop accelerating it, it keeps on going until another force acts upon it. I have the idea that as soon as an object has stopped accelerating and is not interacting with anything else, its mass returns to rest mass, regardless of its now (constant) momentum or speed.
I have come to this conclusion because, if we take an object and want to measure its mesurment or momentum, we need a frame or points of reference in order to complete this task...Lets say we take this same object and accelerate it, during its initial acceleration period, it acquires energy and mass, granted. Now when the object is travelling at a certain speed; take everything else that exists in the universe and make it disappear. Can we now measure the speed or momentum of the object ? No ! Can we say in with certainty that the object is still moving. By frames of reference, no we cannot, by the initial conditions set up at the beginning of the experiment, yes we can. Why does the object keep travelling in that same direction and at the same speed ?
Becasue there are no longer any forces acting up on it. It is balanced and stable. It has returned to its rest mass; regardless of momentum.