178 Chapter 4 Energy
The Relationship Between Work and Kinetic Energy
Let’s examine how we can derive an equation that expresses the relation-
ship between work and kinetic energy. Suppose we continue to impose
force F on a cart in motion, in a direction parallel to that cart’s velocity.
That cart has mass m and starts with an initial, uniform velocity of v.
That means an additional force is imposed on the object in motion.
At this time, the following is true:
work done on the object = Fd
Also, since we’ve represented the final velocity as v
, we can represent the
change in the object’s kinetic energy as the following:
change in kinetic energy = ½ mv
− ½ mv
And since we already know that the change in kinetic energy is equal to
the work done on the object, we can express the following relationship:
− ½ mv
Distance d, the distance that a force is applied