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A child in a wagon seems to fall backward when you give the wagon a sharp pull forward because the force that is exerted on te wagon is greater than the force of the friction pushing the child forward while the wagon is accelerating forward. If the force was great enough or if the wagon were to continue being pushed with a constant or increasing force, the child would eventually fall off the wagon. If the wagon's surface had no friction and there was no wind blowing against the wagon but there was friction on the ground the wagon is rolling on, then the child would stay in the same position and would fall of the wagon if the wagon were to travel far enough. If the surface of the wagon had no friction, there was no other force stopping the wagon, then the child wouldn't move his position while the wagon wouldn't stop ever making it so the child had to eventually fall assuming the wagon is finite and doesn't go all the way around in a circle around a center of gravity.

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