Physically speaking, energy can be defined in terms of the maximum amount of work that can be performed. To explain this more carefully, let us first think about the notion of work. I will only talk about classical physics here.
In classical physics, the motion of objects is governed by Newtons second law
Of course we can vary the force we act on a particle through time, or rather, through the path it takes. We therefore define a quantity we call work, (
Even though we have defined this work in terms of the path along which a force acts, we can work out that the work needed to change the state of a particle from one to another (for instance change the speed of a particle) is only dependant on the initial and final situation. To see this we just work out the integral using Newtons second law.
Now we use
So indeed we only need to know the initial and final velocities and the mass to know the work.
Now we define something called the kinetic energy of an object
Until now we have only talked about moving particles, but there are many other things where we see this quantity of work, think about compression of gas, electric and magnetic fields. However in general it is possible to assign a value to an object that changes when work is being performed. So when we can somehow write down an expression for a value