Kinetic Energy and Work

The kinetic energy of an object is defined as

                           2
     KE  =  1/2 * m * v

The kinetic energy of an object depends on its velocity. To change its velocity, one must exert a force on it. It turns out there's a connection between the force one applies to an object and the resulting change in its kinetic energy:
```
     KE(final) - KE(initial)  =  (force) (distance)
```
where the force is applied over some distance.

We can this combination of force and distance work, so

     KE(final) - KE(initial)  =  Work done on object

In fact, it's a little more complicated than that. Only that component of the force which runs in the same direction as the displacement causes a change in the kinetic energy, so really
```
     KE(final) - KE(initial)  =  (force parallel to displacement) (distance)
```
Another way to write this is with vectors F for force and d for displacement. Then
```
     KE(final) - KE(initial)  =   F  (dot product)  d

                              =   F * d * cos(alpha)
```
where alpha is the angle between vector F and vector d.

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