A particle moves $3 m$ north, then $4 m$ east and finally $6 m$ south. Which of the following are correct about the distance travelled and the displacement?

5m, 13m

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12m, 6m

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13m, 5m

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3m, 5m

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Solution

The correct options are
A
5m, 13m

D
3m, 5m

Let the particle start from A and finally reach B as shown. Distance is the length of the actual path taken by it.
In this case, distance = $3 m + 4 m + 6 m = 13 m$
Displacement is the shortest distance between the initial and final position.
In this case displacement = $A B$
$= \sqrt{(B C^{2} + A C^{2})}$
$= \sqrt{(3^{2} + 4^{2})} m = 5 m$

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