In physics, work is a measure of the amount of energy transferred by a force; for example, if a horse sets a wagon in motion, the horse’s force on the wagon is putting some energy of motion
into the wagon. When a force 
acts on an object that moves in the
direction of the force by an infinitesimal distance 
, the
infinitesimal work done is 
. Integrating both sides, we have
, where the force may depend on 
, and 
and 
represent the initial and final positions of the object.
Example
A spring compressed by an amount 
relative to its relaxed length
provides a force 
. Find the amount of work that must be done in
order to compress the spring from 
to 
. (This is the amount of energy stored in the spring, and that energy will later be
released into the toy bullet.)
The reason 
grows like 
, not just like 
, is that as the spring is com- pressed more, more and more effort is required in order to compress it.
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