Newton's second law describes how force produces acceleration. The same dynamics can be expressed without explicitly following the time evolution: the net work done on an object equals its change in kinetic energy.

$$W_{\mathrm{net}}=\Delta K=K_f-K_i.$$

Interpreting the sign

Positive net work increases kinetic energy, so the object's speed increases.

Negative net work decreases kinetic energy, so the object's speed decreases.

Zero net work leaves the kinetic energy unchanged, although the direction of velocity may still change.

Example

Suppose an object begins with kinetic energy $20,\mathrm J$ and the net force does $15,\mathrm J$ of work. Then

$$K_f=20+15=35,\mathrm J.$$

The theorem relates two states directly without requiring the elapsed time.

Individual forces

The net work is the sum of the work done by all forces:

$$W_{\mathrm{net}}=\sum_i W_i.$$

A force can therefore add energy while another removes it.

The work-energy theorem is not a separate conservation law; it is another form of the relation between net force and motion.