# The potential energy function of a particle in the x−y plane is given by U=k(x+y), where k is a constant. The work done by the conservative force in moving a particle from (1,1) to (2,3):

A conservative force is a force done in moving a particle from one point to another, such that the force is independent of the path taken by the particle. It depends only on the initial and final position of the particle. Gravitational force and elastic spring forces are two such examples of conservation forces.

### Solution

We know that otential energy of a body is its capacity to do work by virtue of its position in a conservative forcefield.So if the body is free to move it will do so in such a way as to reduce its potential energy and the reduction in the potential energy will be equal to the positive work done by the body. If work done by conservative force is positive, then kinetic energy of body will increase. This is because the potential energy decreases and an equal amount of rise would occur in kinetic energy because of law of conservation of energy.

Work done by conservative force =−△U

=Ui−Uf
=[k(1+1)]−[k(2+3)]=−3k

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