1.

A particle moves in xy-plane from position (2m, 4m) to (6m,8m) is 2s. Magnitude and direction of average velocity isA. `sqrt(2) ms^(-1)` and `45^(@)`B. `2sqrt(2) ms^(-1)` and `45^(@)`C. `4sqrt(2) ms^(-1)` and `30^(@)`D. `3sqrt(2) ms^(-1)` and `60^(@)`

Answer» Correct Answer - B
Displacement, `Deltar = r_(2) - 4 hati +4hatj`
`:. v_(av) = (Delta r)/(Delta t) = (4hati + 4hatj)/(2) = 2(hati +hatj) ms^(-1)`
`rArr` Magnitude of velocity,
`|v_(av)| = 2sqrt(1^(2)+1^(2)) = 2sqrt(2)ms^(-1)`
Direction, `theta = tan^(-1) ((Delta v_(y))/(Deltav_(x))) = tan^(-1) ((2)/(3)) = tan^(-1) 1 = 45^(@)`


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