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# A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds from his initial position?

Given, a farmer covers 40 m in 40 s .

So, he will cover 1 m in $$40 \over 40$$ $$= 1 s$$

Now, after 2 min 20 s which is equal to 140 s , he would have covered $$140 \over 1$$ $$= 140 m$$

Case 1: When the farmer starts moving from corner of the field

Then, after 140 s he would have covered $$140 \over 40$$ $$= 3.5$$ rounds of the field.

So, displacement would have been, $$\sqrt{10^2 + 10^2} = 14.1 \ m$$    { By Pythagoras theorem}

Case 2: When the farmer starts moving from middle of any side

Then, after 140 s he will be at the middle of the opposite side of his starting side

So, his displacement will be 10 m.

Case 3: When the farmer starts moving from any random point.

Then his displacement will be in between 10 m and 14.1 m