What happens to a fly floating in the air when the train starts moving I was wondering, within a static train, for a fly which is currently floating in the air and not moving at all, what will happen if:


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*The train starts to accelerate and move forward. Will the floating fly experience inertia and being pushed backward?

*If the train is completely evacuated (without air), will the floating fly experience inertia too?

 A: The fly will experience only whatever forces are acting on it, which is none in a vacuum. The same way a person on ice skates would not experience any forces on him as the train moved forward and he remained stationary. That is because there is no horizontal component of the contact force.
BTW: A fly cannot fly in a vaccum.
A: We needn't think about a train to develop a mental picture of the physics involved - actually, that may over-complicate it. 
Have you ever caught a fly in a bottle? If so, you'll notice that the fly's motion is relatively independent of the bottle's motion - until the fly hits a wall of the bottle, of course. Moving the bottle does (practically) nothing to the fly's motion because the bottle is exerting very (very!!) little gravitational pull on the floating fly. 
So the fly's motion will remain (practically) unaffected by moving the bottle, and a large train is in effect just a much larger container than the bottle, with more room for the fly to move until it hits the wall of a train. 
