
Suppose a constant net force F_{net} acts on an object of mass m over some distance . Newton's Second Law tells us that the object will have an acceleration a = F_{net}/m. If the object's initial velocity was v_{o} and its final velocity is v, kinematics tells us that:
Multiplying both sides of this equation by the object's mass, m, gives:
Rearranging:
Since F_{net }= ma (Newton's Second Law), we can substitute:
then divide both sides of the equation by 2:
This is the Work/Energy Equation. Alternatively, here is an alternate derivation similar to the text's (p. 109).