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Under what conditions can a body travel a certain distance and yet its resultant displacement be zero ?
When a body moves such that it returns to its origin, the distance would be the total length of the path travelled while the displacement would be zero due to no change in position.
These are the following conditions when a moving body travels a certain distance yet the displacement is zero.
1. A body moving along a rectangular path $ABCD$. Let a moving body starts from point $A$ and returns back to $A$.
The displacement would be zero because there is no change in position.
Yet it has travelled a certain distance which is equal to the length of total path travelled
Distance$=AB+BC+CD+DA$
2. When a body is moving along a circular path, and completes one round then the displacement would be zero because there is no change in position. On the other hand it will travel a certain distance which would be equal to the total length of the path travelled.
Let a body starts moving from $A$ and after one complete round it will return to $A$.
Displacement$=$ no change in position$=0$
Distance travelled $=$circumference of the circular path$=2\pi r$
$r$ is the radius of the circular path.
3. When a body moves along a single straight linear path $AB$ from $A$ and then returns to $A$.
Displacement $=0$
Distance travelled $=AB+AB=2AB$
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