# Derivation of Kinetic Energy Equation in a minute | Derive Translational KE equation

Last updated on April 16th, 2021 at 01:11 pm

**The energy possessed by a moving body due to its motion is known as Kinetic Energy. Here we will derive the translational kinetic energy equation** **which goes like this:** **K = (1/2) mV ^{2}**.

So let’s BEGIN.

**How to derive the equation of Kinetic Energy?** | Derive Translational KE equation

Let’s take an object of **mass m** which is at rest. A **force F **is applied to it in such a way that its **final velocity becomes V** and the **displacement** made by it in the direction of the applied force is **S**.

The object has gained kinetic energy due to the motion caused by the applied force.

So we can say that the work done by the force **F** on the object equals the kinetic energy gained by the object.

Work Done on the object by the force **F** = W = FS cos θ ——(1)

Here, θ = 0 degrees, as the displacement S happens in the direction of the force F.

W = FS cos θ= F S cos 0 = FS = m a S ……. (2)

From equation V^2 = U^2 + 2 a S

As Initial velocity U =0,

So, V^{2} = 2 a S

=> S = V^{2} / (2 a) …. (3)

From (2) and (3)

W = m a S

=> **W = m a V ^{2} / (2 a) = (1/2) m V^{2} ** ………..(4)

**As discussed earlier, Kinetic energy K gained by the object= work done on it by the force F = (1/2) mV ^{2} **

**Thus we have derived the equation of KE, which is K = (1/2) mV ^{2} **

## Frequently Asked Questions on KE | Revision

Here are a few FAQs on kinetic energy fundamentals.

### Kinetic Energy Definition

**The energy possessed by a moving body due to its motion is known as Kinetic Energy. **

### Kinetic Energy Formula (Translational)

**The translational kinetic energy equation** **goes like this:** **K = (1/2) mV ^{2}**. This is the formula of Kinetic energy of an object of mass m moving with speed v along a line.

### Kinetic Energy Formula (Rotational)

**The rotational kinetic energy equation** **goes like this:** **K = (1/2) Iw ^{2}**

(It is the Rotational kinetic energy of an object with

**Moment of inertia**I and angular velocity w)

### Types of Kinetic Energy

Kinetic Energy can be of 2 types: (1) Translational Kinetic Energy (2) Rotational Kinetic Energy

### Translational Kinetic Energy definition

The kinetic energy of an object in motion along a line is known as translational kinetic energy.

### Rotational Kinetic Energy definition

Rotational kinetic energy is the energy possessed by an object, like the blade of a wind turbine, rotating about a fixed axis.

It is the kinetic energy of the rotational motion.

## Summary | Take away | Suggested Reading

As we have seen how to derive the equation of the kinetic energy and gone through a few FAQs. Now it’s time to study a few related posts. We suggest you a few posts for your reading. Here are those posts with links.

**How to derive momentum-kinetic energy relationship equation?**

**Work-Kinetic Energy theorem with equation derivation**

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