For simplicity we start off with a simplified one-dimensional world.
Recall the following expression from kinematics
which holds for motion with constant acceleration:
I have secretly been promoting this expressions because it
forms the basis for our definition of energy. It turns out that
to form a useful conserved quantity we multiply the expression by mass:
In going from the first to the second line
we injected what Newton taught us in his second law of motion: F=ma.
The quantity
Is a scalar which characterizes motion. We call it the kinetic energy
of the particle.
We see that the SI units for energy are
I put the subscript f on to indicate that it is
the final state kinetic energy. The initial state kinetic energy
is
Equation 3 states that the final and initial state kinetic
energies differ by an amount
which characterizes what was done to the particle between the initial and
final state: A force F was applied over a distance d.
We say that the force performed work on the particle.
Thus in words I can change the kinetic energy of a particle by
performing work on it with an external force.
This simple expression is our first encounter in physics with the
important concept of energy. We shall find that
energy cannot be created or destroyed but can only
be converted from one form to another. Equation 3
describes a situation in which energy flows from one system
(that which produces the force) to another (the particle with kinetic
energy 
.
Our first examples of the use of energy to analyze problems in mechanics really are thinly veiled application of Equation 1. They serve to introduce a new way of looking at things which can readily be generalized to situations where Equation 1 is not directly applicable. Note however that as a matter of principle Equation 3 came from Kinematics and Newton's laws so there is nothing that I can do with the concept of energy which I could not in principle do by applying kinematics and Newton's laws.