A particle moves in xy-plane from position (1m,2m) to (3m,4m) in 2s. Find the magnitude and direction of average velocity.

Options

A. `sqrt(2) ms^(-1)` , `60^(@)`
B. `sqrt(5) ms^(-1)` , `45^(@)`
C. `sqrt(12) ms^(-1)` , `45^(@)`
D. `sqrt(2) ms^(-1)` , `45^(@)`

Answer

D

Explanation

Given, positions of the particle are
`r_(1) = x_(1) hati + y_(1) hatj = hati +2hatj`
and `r_(2) = x_(2) hati +y_(2) hatj = 3 hati +4 hatj`
Displacement, `Deltar = r_(2) - r_(1) = 2hati +2hatj`
`:.` Average velocity, `v_(av) = (Deltar)/(Delta t) = (2hati + 2hatj)/(2)`
`rArr |v_(av)| = sqrt((1)^(2)+(1)^(2)) = sqrt(2) ms^(-1)`
Direction of average velocity with x-axis
`theta =tan^(-1) ((Deltav_(y))/(Deltav_(x))) = tan^(-1) ((1)/(1)) = 45^(@)`