There are some easy derivations for the work done by common forces. The work done by a constant gravitational force is pretty simple. The force exerted by a constant gravitational force is just and the displacement in the direction of the force is just the change in height , hence

- Work done by constant gravitational force:

The force exerted by a spring is given by Hooke’s Law, , now this force varies with extension (which is essentially the displacement). Hence, we can’t simply take the product, we have to take the integral of with respect to , i.e

- Work done by spring:

The work done to accelerate an object from rest to a velocity is called the *Kinetic Energy* of the object. Now the force needed to accelerate the object is, by Newton’s second law:

Since the work done by is

Hence,

- Kinetic Energy of an object:

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