Overview
Formulation
Define the kinetic energy of a particle as
{% KE = \frac{1}{2} m v^2 = \frac{1}{2} m \vec{v} \cdot \vec{v} %}
{% m \vec{v} \cdot \frac{d \vec{v}}{dt} = \frac{d}{dt} (\frac{1}{2} m v^2)%}
This implies that the work done is equal to the change in the kinetic energy.
{% W = \Delta KE %}
This is sometimes referred to as the
work-energy theorem