A time bomb put inside a box is left into the vacuum: it explodes...the box coverings starts moving
I want to ask: is the force behind sudden acceleration internal or external
I am confused about when to call the force internal or external based on Newton's first law of motion. It says a body maintains the state of rest or motion until acted upon by an external force. My guess is its external force,otherwise it would violate Newton's law but it looks internal
Answer
The answer is it depends on how you want to look at it. You first need to define the object whose motion you want to follow. Once that's done you can decide what is an internal or external force.
Suppose you're interested in a piece of a panel of the box (that flies off in the explosion). If this is your "system", then the bomb is clearly external - it's not part of that little piece of box panel. If you set it up "at rest", when the bomb goes off it starts moving because of this external force, and Newton's law is not broken.
Alternately, you might be interested in the motion of then entire box-bomb system. Obviously this is going to end up in little pieces when the bomb goes off, but that's ok, we can still ask about the motion of the centre of mass of all those little bits of box and bomb. Now the force is clearly internal to the system, and if you tracked things carefully, you'd find that all the different pieces fly off in different directions in such a way that the centre of mass does not accelerate. Internal force, stays at rest (or constant velocity), so Newton's law is ok again.
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