A particle moves in x-y plane from (0,0) to (a,a) and is acted upon by a force `vecF=k(y^(2)hati+x^(2)hatj)N`, where k is a constant and x and y are coordinates in meter. Find work done by this force, if the particle moves along
Two straight lines first from (0,0) to (a,0) and then from (a,0) to (a,a)

Explanation

`dW=vecF.dvecs=k(y^(2)hati=x^(2)hatj).(dxhati+dyhatj)`
`=ky^(2)dx+kx^(2)dy`
when it moves from (0,0) to (a,0)
y = constant = 0 implies `dy = 0`
`therefore dW_(A)=k(0)dx+kx^(2)(0)`

= 0
`impliesW_(A)=intdw_(A)=0`
When it moves from (a,0) to (a,a)
x = constant = a implies `dx = 0`
and y changes from 0 to a
`therefore dW_(B)=ky^(2)(0)+ka^(2)dy=ka^(2)dy`
`therefore W_(B)=ka^(2)underset(0)overset(a)intdy=ka^(3)`
`therefore W=W_(A)+W_(B)=ka^(3)`