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gives the relationship between the initial ( ) and final ( ) velocities, when a body moving with a constant acceleration ( ) moves through a certain distance ( ).
The easiest way to derive it is to use the Work-Energy Principle, which states that the work done on a body is equal to the increase in its Kinetic Energy. Thus, if a constant force acts on a body of mass , giving it a (constant) acceleration , we have:
and so if the body now moves through a distance in the direction of the force, the work done on the body is:
This increases the body's KE from to , where and are the initial and final velocities. So, using the Work-Energy Principle, we have: