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Can a body undergo some displacement without travelling any distance? 


No, it is not possible for a body undergo some displacement without travelling any distance. 
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A particle moves from A to B along three different paths. Is the displacement along three paths different?

Can a body travel certain distance without undergoing any displacement?

How does the displacement of a particle change, when reference point for the position is shifted?

Can the distance travelled by a particle be negative?

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