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An object has a displacement from positi...

An object has a displacement from position vector `vec(r )_(1)=(2hat(i)+3hat(j))m` to `vec(r )_(2)=(4hat(i)+6hat(j))m` under a force `vec(F)=(3x^(2)hat(i)+2y hat(j))N`. Find the work done by this force.

Text Solution

Verified by Experts

`W=underset(bar(r_(1)))overset(bar(r_(f)))intvec(F).dvec(r)=underset(bar(r_(1)))overset(bar(r_(2)))int(3x^(2)hat(i)+2yhat(j)).(dxhat(i)+dyhat(j)+dzhat(k))`
`underset(2)overset(4)int3x^(2)dx+underset(3)overset(6)int2y dy = [x^(3)]_(2)^(4)+[y^(2)]_(3)^(6)=83j`
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