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Question

Ratio of the magnitude of displacement and the distance is equal or less than 1.Explain.


Solution

We know that displacement is the body’s overall change in position from the initial point. Even if the body has traversed, the displacement of the body can be zero.

Although for distance, this is not true. If a body has moved, the distance can never be zero.

For example, if I run a circle and come back to the initial point, then my displacement would be zero, but the distance I covered would be the circumference of the circle.

Therefore my displacement would always be either equal(straight line path), or less(the above circle example) than the distance and therefore the ratio of displacement to distance would always be less than one.

P.S : Note that the displacement does not have to be zero necessarily, to be less than distance.

If I traverse half a circle, then my distance would be (pi)(r), though my displacement would be the straight line distance from the initial point to the final point, which would definitely be less than the distance, because, straight line path is the shortest path

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