Work-Energy Theorem

The work energy theorem is a way of connecting the Work done on an object to it’s Kinetic Energy.

$$W=\Delta K$$

Derivation §

Using Newton’s Second Law of Motion and kinematic equations. we can derive the connection to work and kinetic energy. Assume we have a system with a single object with mass $m$, acted on with a constant net force, $F$. Since the force and mass are constant, so is the acceleration:

$$a=\frac{F}{m}$$

We can use the kinematic equations (as $a$ is constant):

$$v^2=u^2+2as$$

• $v,u$ = Final, initial velocity
• $a$ = Acceleration
• $s$ = Displacement

$$v^2=u^2+\frac{2Fs}{m}$$

$$Fs=\frac{m}{2}(v^2-u^2)=\frac{m}{2}{v}^2-\frac{m}{2}{u}^2$$

$Fs$ is Work done ($s=x$) and the formula for kinetic energy is $K=\frac{m{v}^2}{2}$. So:

$$W=K_f-K_i=\Delta K$$