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

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) mV2.

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, V2 = 2 a S 
=> S = V2 / (2 a) …. (3)

From (2) and (3)
W = m a S
=> W = m a V2 / (2 a) = (1/2) m V2 ………..(4)

As discussed earlier, Kinetic energy K gained by the object
= work done on it by the force F = (1/2) mV2

Thus we have derived the equation of KE, which is K = (1/2) mV2

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) mV2. 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) Iw2
(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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Derivation of Kinetic Energy Equation in a minute | Derive Translational KE equation
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