The beauty of the expressions above is that they cut through details of motion to yield relationships between initial and final state properties. Here is an example of a problem that you could not solve without these expressions.
A child comes to an emergency ward after a playground accident. He slid head first down a slide and impacted a stone on the ground head first. To estimate how serious the injury might be you want to know the speed at impact.
If you know how to use the work kinetic energy theorem
the only question you need to ask is:
``How far above the ground did the child start sliding down?''
If you can assume that
the slide is very slippery, you do not need any more details about the nature of the
slide just the initial height over the point of impact.
The reason is that only gravity does work under these
circumstances. Normal forces from the
slide are present but by definition normal forces do no work since
they are perpendicular to the displacement at all times. The dot product in the
expression for work thus vanishes:
and therefore only gravity does work.
The work kinetic energy theorem reads
Where
contains the velocity we are interested in. Assuming that 
ie. that there as no initial velocity then we have
In other words we are dealing with the equivalent of a free fall head first
from the height of the slide.