The basic definition of work is . This form of the work allows us to obtain a quantity that has significant meaning in physics. That is, starting from Newton's second law of motion, , the work done by the force along the displacement is
In the last equality, the acceleration and displacement are considered in the same direction; therefore, their scalar product is the same as the algebraic product of their magnitudes (hyperlink to general calculus). The expression for the work can be rewritten using the relation for uniform accelerated motion, . From where, . Thus, the work is
In the previous expression, the effect of work is to change the quantity to . This quantity is called the kinetic energy of the object moving at the velocity ,
Notices that the kinetic energy of an object is always a positive quantity and independent of the direction of motion. In addition, the kinetic energy of an object is not an absolute property of the object. In fact, the kinetic energy of an object is relative to the observer's frame of reference.
At the same time, the effect of ball hitting an object inside the bus is clearly weaker than the effect of the ball hitting an object outside the bus. Thus, this simple example illustrate that the kinetic energy is relative to the observer. The unit of Kinetic Energy is the same as the unit of Work. In fact, Unit of Kinetic Energy = (Kilogram) (Meter/Second)^{2} = (Kilogram) (Meter/Second^{2}) (Meter) = (Newton) (Meter) Unit of Kinetic Energy = Joule This result should be expected because the difference between the final and initial kinetic energy is the work and only quantities of the same nature can be added or subtracted. The mathematical expression shown above, , is called the workenergy theorem because this formula establishes the relation between the work and the kinetic energy,
This relation can be read in different forms,
The change in kinetic energy is an observable that can be measured experimentally for all classical objects; then, the change in kinetic energy is the result of all forces acting on the object such as external agent applying forces, frictional forces, normal force, or gravitational force. Thus, The change in Kinetic Energy of a system is equal to the Net Work acting on the system even when the actual forces acting on the system may be various or only part of one of the forces is the responsible of the change (see application below).

