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This question already has an answer here:

Suppose there is a train moving right with constant acceleration and there is a butterfly inside the train which moves opposite to direction of motion of train i.e. towards left. The butterfly always moves with constant velocity outside the train.

Does the butterfly retard or accelerate inside the train due to acceleration of train or does it move with constant velocity easily? Please explain.

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marked as duplicate by Nathaniel, Dilaton, Brandon Enright, John Rennie, jinawee Feb 25 '14 at 8:42

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The equivalence principle tells us that to some one sitting in the train, it looks like the acceleration due to gravity has a new term which points opposite to the direction of acceleration of the train. This new gravity force would cause the butterfly to accelerate to the back of the train until it reaches its terminal velocity (I think the terminal velocity would be reached quickly).

Notice that there will also be a buoyant force acting on the butterfly which points to the front of the train. In fact if the butterfly were instead a balloon, so that it was less dense than the air, then the net horizontal force would be in the direction of acceleration.

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