The Work-Energy Theorem is a simple idea in physics. It tells us that when we do work on an object, that work changes the object's kinetic energy.

Kinetic energy is the energy an object has because it's moving. We can write this idea as:

Work = Change in Kinetic Energy
(W = ΔKE)

Here, the change in kinetic energy is the difference between the energy when it stops moving and when it starts. We can show this using:

Final Kinetic Energy - Initial Kinetic Energy
(KE_f - KE_i)

Kinetic energy itself can be calculated with this formula:

Kinetic Energy (KE) = 1/2 * mass (m) * velocity squared (v²)

In this formula, "mass" is how much stuff is in the object, and "velocity" tells us how fast the object is moving.

Another important type of energy is potential energy (PE). This is the energy an object has because of its position. For example, when we think about gravity, we can find gravitational potential energy with this formula:

Potential Energy (PE) = mass (m) * gravity (g) * height (h)

In this formula, "height" is how high the object is above a certain level.

Now, let’s talk about total mechanical energy (TME). In a closed system, which is like a little world where no energy can get in or out, the total energy stays the same. We can say:

Total Mechanical Energy (TME) = Kinetic Energy (KE) + Potential Energy (PE)

When we do work on an object, we can change its potential energy into kinetic energy or the other way around. A good example is when something falls. As it falls, its potential energy goes down because it is getting closer to the ground, while its kinetic energy goes up because it moves faster.

To sum it all up, the Work-Energy Theorem shows us how kinetic and potential energy are connected. It reminds us that energy can shift between different forms but the total energy stays constant in a closed system. This means:

Work = Change in Kinetic Energy + Change in Potential Energy = 0
(W = ΔKE + ΔPE = 0)

So, energy is always there; it just changes from one form to another!