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How can a body have velocity without displacement?

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Yes it is possible for a body to have zero displacement but non zero velocity. This would be the case for example of a body moving in in circular motion. Every time the object returns to its original position, its displacement will be zero. however, it will be moving with certain velocity. Another example is an object that is launched vertically upwards in is moving only under action of the gravity force. When the object returns to the same point from where it was launched, it will have zero displacement and certain velocity.

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