A force is said to do work when it acts on a body and results in a displacement in the direction of the force. It is a scalar quantity defined by
`W = vec F * Delta vec d = FDelta dcos theta`,
and it is measured in joules (J). Work can be zero in three situations: when force is zero, when displacement is zero, or when force and displacement are perpendicular. When the angle between force and distance exceeds 90º, work becomes negative. On a force-position graph, the area under the curve represents work.
Kinetic energy is energy due to motion. For an object moving at speed `v`, kinetic energy is defined as the amount of work needed to accelerate the object from rest to `v`. The formula for kinetic energy is
`E_"k" = 1/2mv^2`.
A change in kinetic energy represents work being done:
`W = Delta E_"k" = 1/2mDelta v^2`.
We can also relate kinetic energy to momentum with
`E_"k" = p^2/(2m) qquad and qquad p = sqrt(2mE_"k")`.