Kinetic Energy Formula: Derivation, Types & Solved Examples

Kinetic Energy Formula in physics is used to measure the amount of work done by an object or a particle due to its motion. When an object is subjected to a net force, it accelerates and gains kinetic energy. As we know the principles and applications of science are everywhere. Similarly, the application of kinetic energy can be seen in our daily life activities like walking, jumping, throwing and falling.

• The kinetic energy formula is a property of a moving object defined by both its mass and velocity.
• Kinetic energy is a scalar quantity that is described by only magnitude.
• It is equal to the work which is needed to accelerate an object.
• The energy is calculated when the object is at rest till the object is in motion.

In physics, Kinetic Energy Formula is expressed as 

\(K\,E= {{1 \over 2}mv^2}\)

Here,

• KE is the kinetic energy,
• m is the mass of the body, and
• v is the velocity of the body.

Read More: Center of Mass

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What is Kinetic Energy?

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Kinetic Energy is the energy acquired by an object as a result of its movement or motion. The formula is used to calculate the amount of work necessary to accelerate a body of a specific mass from rest to a given velocity.

• When an object accelerates due to the force applied to it, it produces kinetic energy.
• Kinetic energy formula is affected not only by motion but also by the mass of the object.
• It can be transferred between objects and can also be transformed into other kinds of energy.
• The SI unit of kinetic energy formula is Joule (J).
• It is a scalar quantity as it has only magnitude. 
• The dimensional formula of kinetic energy is [M¹ L² T^-2].

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Kinetic Energy Formula

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Kinetic Energy Formula is used to calculate the mass, velocity, or kinetic energy of a given body. The formula is derived from a Greek word named kinesis, which means motion. 

• Gottfried Leibniz and Johann Bernoulli invented the Kinetic Energy Formula.
• It depends upon the object's mass and speed.
• The energy is a scalar quantity that is defined by its magnitude.
• The SI unit of the formula in the CGS system is erg.

Kinetic Energy Formula is given as 

\(K\,E= {{1 \over 2}mv^2}\)

• where, KE: Kinetic Energy
• m: Mass of the Object
• v: Velocity of the Object

Read More: Work, Energy and Power Formula

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Derivation for Kinetic Energy Formula

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In order to derive the Kinetic Energy Formula, consider the example of an object of mass m which is at a state of rest on a table.

• Force F acts on the object making it move distance S. Thus,
• Work Done = F x S

W = F_net x S -------- (1)

• Now consider that the work done on the object results in a change in velocity from u to V. Let “a” be the acceleration.
• Using the equations of motion, 
• V²- u² = 2as

s = V²-u²/2a --------- (2)

• Using Newton’s Second Law of Motion, 

F = ma -------- (3)

• From equations (1), (2), and (3), we get

W = ma x (V²-u²/2a) = (1/2)m(V²-u²)

• Since the object is in a state of rest, u=0

W = (1/2)mV²

• Lastly, the kinetic energy of an object moving with a certain velocity is equal to the work done on the object. Thus, 

Kinetic Energy Formula = 1/2 mV²

Read More: Unit of Force

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Transformation of Kinetic Energy

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Kinetic energy is a type of energy that can be converted into other types of energy and exchanged between objects. The work is said to be done when a force is applied on it. 

• Kinetic Energy Formula is applicable from low to high speeds.
• The total energy is dependent upon the sum of kinetic energies resulting from different types of motion.
• The kinetic energy depends upon the work and force.
• Cycling, roller coaster and running are some daily life examples of kinetic energy.

Read More: Work-Energy Theorem

Kinetic Energy Transformation

Read More: Work, Energy and Power

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Types of Kinetic Energy

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Kinetic Energy are can be classified into various types which are as follows:

Radiant Energy

Radiant Energy is a form of kinetic energy that is constantly moving through a medium or space. The energy is radiated from matter to the surrounding. Some examples of radiant energy are as follows:

• Gamma Rays
• Ultraviolet Light

Thermodynamic Energy

Thermal Energy, often known as heat energy, is created when atoms collide. It is depended upon the temperature and heat of the material. Some example of thermal energy are as follows:

• Natural Hot Springs
• Heated Swimming Pool 

Sound Energy

When an object vibrates, sound energy is produced. In a vacuum, sound energy travels through the medium, but there are no particles to act as a medium. The energy cannot travel in vaccum or space. Some example of sound energy are as follows:

• Tuning Forks
• Beating Drums

Electrical Energy

Electrical energy is provided by free electrons, both positive and negative in charge. The energy created is transfered to other devices. It is used in many electrical devices. Some examples of electrical energy are as follows:

• Used Batteries 
• Lightning

Mechanical Energy

Mechanical Energy is the combination of kinetic and potential energy. It cannot be created or destroyed but can be converted from one form to another. Mechanical energy can be shown in the following examples:

• A satellite orbiting around the Earth.
• A Moving Vehicle.

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Things to Remember

• Kinetic Energy is the energy an object gains as a result of its movement.
• An item accelerates and acquires kinetic energy when a net force is applied to it.
• Kinetic Energy Formula is affected by the mass and speed of an object.
• It is a scalar quantity measured in Joules.
• Kinetic Energy Formula is given as \(K\,E= {{1 \over 2}mv^2}\).
• Mechanical Energy, Electrical Energy, Sound Energy, Thermodynamic Energy, and Radiant Energy are the types of Kinetic Energy.

Read More: Relation between ev and joule

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Previous Years’ Questions 

1. The dimensions of kinetic energy are… (KEAM)
2. If the kinetic energy of a body is increased by 300% then the percentage… (JKCET 2017)
3. The kinetic energy of a particle moving along a circle… (UP CPMT 2011)
4. The kinetic energy k of a particle moving along a circle of radius… (JIPMER 2001)
5. The kinetic energy of a body of mass 4 kg and momentum… (KCET 2015)
6. A running man has half the kinetic energy of that a boy of half… (Punjab PMET 2001)
7. The total energy of the body executing simple harmonic motion…
8. If the kinetic energy of a body becomes four times its initial value… (AIIMS 1998)
9. A ball whose kinetic energy is E is projected at an angle… (AIEEE 2002)
10. The kinetic energy of a particle executing simple harmonic… (JKCET 2006)