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.

An object has a displacement from position vector vec(r )_(1)=(2hat(i)

1.	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.
Answer» Solution :`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`