Particle of mass m moving from point A to point B
We say that a body has kinetic energy (Ec) when it has mass and speed. More specifically, we say that this kinetic energy corresponds to the work done on the body . But how could we represent this kinetic energy in terms of m and v ?
Let us consider a particle whose mass is m , which passes through a point A with speed ; and by a point B with velocity ; along any trajectory, under the action of any number of forces. We can determine the total work done by these forces between points A and B through the following equation:
Based on this result, it is reasonable to assume that the kinetic energy of a body of mass m and speed v is given by:
Thus, we can say that in the first equation the factor m . v 2 B /2 is the kinetic energy at point B (E cB ); and m. v 2 A /2 is the kinetic energy at point A (E cA ). In this way, we can write the first equation in another way:
τ AB = E cB – E cA = ∆E c (change in kinetic energy)
Therefore, we can say that these equations are mathematical ways of stating the Kinetic Energy Theorem, which says:
The total work of the forces acting on a particle is equal to the change in the kinetic energy of that particle.
Note: if this total work is positive, there will be an increase in kinetic energy; if it is negative, there will be a decrease in kinetic energy.