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OK, there is an "unstoppable" object which is moving towards an "unmoveable" object.
OK, I may need to be corrected on this but I think that the energy is from both mass and kinetic energy to heat. I know the first atom bomb was made by having plutonium(?) hemispheres blasted by conventional explosives towards each other. The hemispheres are machined to very exacting tolerances so that they fit together very precisely. When the conversion to heat occurs, the air ruching back into the void created by the fission process causes the blast, just as when lightening makes thunder, but on a much, much large scale.Now, can you figure out how I tricked you into accepting this answer? 
I think it's simpler than that:QuoteOK, there is an "unstoppable" object which is moving towards an "unmoveable" object. The existence of one negates the possibility of the existence of the other. In other words, whatever science you suspend in imagining the one, must automatically prevent the other from coming into being. Like many classic pardoxes this question turns out to be linguistic rather than physical...Batroost (the cynic). 
The hemispheres are machined to very exacting tolerances so that they fit together very precisely. When the conversion to heat occurs, the air ruching back into the void created by the fission process causes the blast,
What does unstoppable and unmovable actually mean?There can not be any absolute frame of reference where one thing is regarded as stopped, and another regarded as moving. All motion is relative. A thing is only stopped, or only moving, in relation to some particular observer.To say something is unmovable is merely to say that the particular observer will be in a permanently fixed position with regard to that object - other observers might still see that object as moving.I assume when you talking about an unstoppable object, you actually mean more than merely unstoppable, but an object which cannot alter its speed relative to you at all (e.g. it has some of the attributes of light travelling through a vacuum). If all you mean by unstoppable is that it can never have zero velocity relative to you, but is quite capable of bouncing back the way it came, then that does not of itself in any way preclude the immovable object (although there would be other physical laws that would make the idea of an immovable object rather difficult).
So who is stationary and who is moving?