I had a tough time deriving formulas for mechanical energy when given in school as assignment or as a question in exams. I don’t want any of you reading this to experience the same feeling. So, I would like to show you how we derive the conventional formulas for potential and kinetic energies to be later used in problems.

## Potential Energy

We know that **Work** is equal to the product of the **Force** applied and the **Distance** travelled. So,

W = F x s

Also, **Force** is equal to the product of **Mass** of the body and the **Acceleration**. So,

W = ( m x a ) x s

Now, as the energy is being calculated on Earth, we have to substitute Acceleration with ** g **( acceleration due to gravity ) and the Distance with

*( height ). So,*

**h**

W = ( m x g ) x h

Therefore, we have derived our formula i.e.

W = m g h or E_{K}= m g h

## Kinetic Energy

We know that **Work** is equal to the product of the **Force** applied and the **Distance** travelled. So,

W = F x s

Also, **Force** is equal to the product of **Mass** of the body and the **Acceleration**. So,

W = ( m x a ) x s

Now, the Distance can be substituted with ( *v ^{2} – u^{2} / 2 a* ) from the third equation of motion (

*v*)

^{2}– u^{2}= 2 a sW = ( m x a ) (

v)^{2}– u^{2}/ 2 aW = m (

v)^{2}– u^{2}/ 2W = ½ m ( v

)^{2}– u^{2}

Usually, the bodies start from rest i.e. *u = 0*. So,

W = ½ m v

^{2}

Therefore, we have derived our formula i.e.

W = ½ m v

^{2 }or E_{P}= ½ m v^{2}

I hope that I have been able to explain the steps to be followed while deriving the equations. 🙂