Consider a force F → = - x i ^ + y j ^ . The work done by this force in moving a particle from point A 1,0 to B 0,1 along the line segment is : (all quantities are in SI units)

Step-by-step solution

It is given that a force F → = - x i ^ + y j ^ acts on a particle. The particle is moved from point A 1 , 0 to B 0 , 1 along the line segment. Work done by a variable force on the particle, W = ∫ F → · d r → = ∫ F → · d x i ^ + d y j ^ (In two dimension, d r → = d x i ^ + d y j ^ and it is given F → = - x i ^ + y j ^ ) W = ∫ - x i ^ + y j ^ · d x i ^ + d y j ^ = ∫ - x d x + y d y = ∫ - x d x + ∫ y d y . As the particle is displac