Work and energy: an alternative approach to motion

When we are interested in the final speed of an object under the effect of a force or several forces, we can choose between two different approaches.

One is to calculate the net force, determine the acceleration and from the acceleration, the velocity. The disadvantage of this approach is that when the motion is not special (such as linear motion with constant acceleration) we need to apply integration to obtain the velocity and the position.

The other approach is to calculate the total work done on the object, which, according to the work-kinetic energy theorem, is equal to the change in kinetic energy. The advantage of this method is that it yields the final speed directly, without our having to know what happened in between.

If all the forces are conservative, potential energy can be used instead of work, which has a further advantage: we do not need to know the path, only the initial and the final position.