In this article, we will learn what is Kinetic Energy, its Definition, meaning, formula, equation, examples, diagram, types, unit, etc.

## What is Kinetic Energy? Definition, Meaning, Examples

### Kinetic Energy Definition

The origin of the word kinetic energy can be traced back to the French word travail mécanique (which means mechanical work) or quantité de travail (meaning quantity of work). Kinetic energy is a form of energy a body possesses while in motion. It may also be defined as the energy contained by mass in motion. It’s a property unique to moving objects and bodies. The motion may be translational, vibrational, or rotational motion.

### Kinetic Energy Meaning & Examples

Energy in science or physics is defined as the capability to do work. It may exist in different forms, but all forms are associated with motion. The two broad categories are potential energy (P.E) and kinetic energy (K.E).

- The former is concerned with bodies in motion, while the latter is associated with objects at rest. Kinetic energy can exist in different forms, further discussed in-depth in the types of kinetic energy section.
- Moreover, the quantity is scalar and always positive because it is an energy form and doesn’t depend on the direction. So, it only has magnitude but no direction. Work is a significant factor while considering kinetic energy.
- If a net force “F” is applied to an object, it will speed up and gain kinetic energy. Hence, the capability to do work is the essential property of kinetic energy.

## What are the Units of Kinetic Energy?

In System International, the unit of energy is Joule “J,” after James Prescott Joule, an English physicist. According to the equation of kinetic energy i-e ½ mv^{2}, we can write units such as kg for “m” and m^{2}/s^{2 }for “v^{2}”, we get joule equal to kilogram times meter square divided by the second square (kg x m^{2}/s^{2}). Calorie represented as “cal” is another most commonly used unit for energy.

One calorie equals 4.184 J. since kinetic energy is a form of energy, it is also expressed in joule or calorie. Whereas in English, the unit for kinetic energy is foot-pound, represented as” ft-lb.” kilowatt-hour (Kwh) is another unit to measure the electricity in a household. 1-kilowatt hours equals 3.6 million joules.

## Examples of Kinetic Energy

There are numerous examples of kinetic energy that we often observe in our everyday life. Any object or body having mass (or apparent mass) and is in motion has kinetic energy. Very few examples of kinetic energy are given below:

- Rubber bands
- Planets
- Light traveling from the sun to planet Earth
- Electrons that orbit atomic nuclei
- Sound from stereo speakers moving towards your eardrums
- A falling meteor
- Satellites orbiting around Earth
- Flowing electricity through a wire
- A waterfall, a flowing river, or flowing stream
- Wind
- An avalanche
- Rolling clouds in the sky
- Airplane flying high in the sky
- A flying bird
- Exercising, walking, jogging, cycling, swimming
- Launching of rocket
- Throwing ball
- Driving a car or any vehicle
- Falling object
- Spinning windmill

## Kinetic Energy Formula or Equation & Derivation

### Kinetic Energy Formula or Equation

In Physics, particles in motion possess more energy than those at rest. Quantitatively, the energy of moving objects is given by the following equation:

**K.E = ½ mv^{2}**

^{ }Where “m” is the mass and “v” is the velocity of the body. The kinetic energy of a particle or system of particles can increase, decrease, or remain constant with passing time.

According to the equation i.e. K.E= ½ mv^{2}, kinetic energy depends on two quantities, they are mass and velocity. Kinetic energy is directly proportional to the object’s mass and the square of the object’s velocity. Hence these two factors affect the kinetic energy of a body. Although velocity is an important aspect, it is dependent upon the mass of the body. The mass will determine how fast or slow a body moves. Velocity in the equation of K.E is squared; therefore, it has exponential effects. Doubling mass will double K.E., but doubling velocity will quadruple the value of kinetic energy.

### Kinetic Energy Derivation

The derivation for the kinetic energy equation is given below using two methods: derivation using algebra and derivation using calculus.

#### Kinetic Energy Derivation Using Algebra

Let’s consider the amount of work done in giving velocity to a body from a state of rest. Now Suppose,

- m= mass of the body at rest
- u= initial velocity of the body
- v= velocity gained by the body
- F= applied force
- a= acceleration produced in the body

the equation is: K∆S = W = m∆a……. (1)

Now we have the third equation of motion:

- V
^{2}– u^{2}= 2as - a= v
^{2}-u^{2 }/2s……. (2)

∵ F = ma… (3)

Now putting the value of “a” in eq (3)

- F = m x (v
^{2}– u^{2}) / 2s…. (4)

Combining eq (1) and (4), we get:

- ∆K = m (v
^{2}– u^{2}) / 2…. (5)

Putting u=0 in eq (5) we get:

- ∆K = m (v
^{2}/2) …… (6)

Work on a body is done if force “F” is applied to a body at rest and it moves through a distance “d.” the equation for work done is:

W=Fd….…. (7)

Now putting u=0 in eq (2), we have: a= v^{2}/2s

we know, F=ma

hence, F=m (v^{2}/2s)

putting this value of “F” in eq (7), we get:

- W = m x v
^{2}/ 2s x s - W = 1/ 2 x m x v
^{2} **W=K.E = 1/ 2 x mv**^{2}

#### Kinetic Energy Derivation Using Calculus

Let’s suppose;

- m = mass of a body
- u = Initial velocity of the body
- F = applied force on the body in the direction of motion
- ds = displacement covered by a body in the direction of motion

The small amount of work done by the force will be:

- dW = F. ds = F ds Cos 0° = Fds (∵ Cos 0° = 1)
- dW = F ds = ma ds (∵ F = ma) (a is an acceleration produced by the force)
- dW = m (dv /dt) ds (∵ a = dv / dt)
- dW = m (ds /dt) dv
- dW = m v dv (∵ v = ds /dt)

Total work done by the force that increases the velocity of the body from u to v is:

- W = ∫
_{u}^{v}m v dv - W = m v (1+1)/ (1+1) |
_{u}^{v} - W = m v
^{2}/2 |_{u}^{v} - W = 1/ 2 m (v
^{2}– u^{2}) - W = 1 / 2 mv
^{2}– 1/ 2 m u^{2}…… (7)

#### Work energy theorem

Work done= final kinetic energy- initial kinetic energy

W= change in K.E

Work done by applied force is a measure of change in K.E of the body hence proving the work-energy principle.

On putting u = 0 in eq (7), we get that:

W = 1/ 2 m v^{2}– 0

^{ }

These were the two methods for deriving kinetic energy. We conclude a few aspects. Firstly, the force does work on the body and K.E increases by the same amount. Hence, according to this phenomenon, work and energy are equivalent to one another.

Secondly, force is a must for changing kinetic energy. Additionally, if the resultant force is perpendicular to the velocity of the object or particle, K.E won’t change.

## Calculation of Kinetic Energy

According to the formula of kinetic energy, it’s easy to calculate the value in case of any given problem. Some examples are given below:

#### Kinetic Energy Solved Problem#1

**Problem**: A person weighing 70 kg is moving at a speed of 1.5 m/s. Calculate the kinetic energy of the person while walking.

__Solution:__

K.E= ½ mv^{2}

Putting the values in equation:

K.E= ½(70 kg)(1.5 m/s)^{2}

K.E= 78.75 kg.m^{2}/s^{2}

K.E= 78.75 J

#### Kinetic Energy Solved Problem#2

**Problem: **A body having kinetic energy of 1000 J is moving with a velocity of 15 m/s. What is the mass of the body?

__Solution__

As we know,

K.E= 1/2 mv^{2}

Rearranging the actual equation:

m= 2K.E/v^{2}

m= 2(1000)/ (15)^{2}

m= 2000 kg.m^{2}. s-^{2}/ 225 m^{2}/s^{-2}

m= 8.88 kg

## How to Convert Potential Energy into Kinetic Energy?

The Gravitational potential energy changes to kinetic energy when an object falls. The relationship is for calculating the speed of the falling object. The gravitational potential energy for a body of mass “m” at height “h” near the Earth’s surface. The equation is as under:

**P.E = mgh**

Where “m” is the mass of the body under consideration, “g” equals 9.8 m/s2 and “h” is the height of the body. Putting all the values in the equation gives the potential energy in joules. The potential energy is further convertible into kinetic energy also. The equation to do so is as under:

**P.E = K.E****P.E = ½***mv*^{2}

Rearranging the formula and putting velocity on one side will give the value of speed. Putting the respective values in the above equation for calculating the velocity “v” will give a value in m/s. That is how potential energy is converted to kinetic energy for a falling object and is calculated using the equation P.E = ½*mv*^{2 }

## First Law of Thermodynamics

The branch of Physics dealing with energy and the work of a system is termed Thermodynamics. The branch deals with the relationship between heat and other forms of energy. The first law of thermodynamics is simple if stated in theory but very deep and consequential in reality.

It says that energy can neither be created nor destroyed but can only be transformed from one form to another, and this way, the system’s total energy remains constant. In generalized form, it means the total energy of the universe remains constant.

The law is related to energy. Kinetic energy is also a form of energy. Hence, the law applies to kinetic energy also. For better understanding, consider a simple example. A pen is placed on the table. Suppose it falls, the stored potential energy converts into kinetic energy. This way, the energy transforms from one form to another, but the total amount of energy remains constant.

## Newton’s Second Law of Thermodynamics

Newton’s second law of thermodynamics is also known as conservation of energy, and it applies to kinetic energy. It states that the quality of energy degrades with time. It means that during every conversion if energy is transformed or transferred, a significant amount is wasted. Kinetic energy is converted into potential energy and vice versa, and it is also harnessed; hence it is always conserved. But energy is lost along the process.

## Kinetic Energy can be Stored

We already know bodies possess it in motion. As per the first law of thermodynamics, energy can neither be created nor destroyed but can only be transformed from one form to another. In both situations, energy is converted into potential energy i.e. it’s not doing work but has the ability or potential to do it. For example, a book lying on a shelf possesses potential energy. But when it is dropped, it is converted to kinetic energy. Hence, we say that kinetic energy can be stored in the form of potential energy.

## Kinetic Energy can be Transferred

Collisions can be elastic or inelastic, which can transfer kinetic energy from one body to the other. One typical example of elastic collision is one billiard ball hitting the other. If we neglect friction between balls and table, then in this ideal situation, balls’ kinetic energy after collision remains equal to the kinetic energy before collision.

While in case of an inelastic collision, consider a moving car bumping into a similar stationary car. In this case, the total energy remains the same but the mass of the new system doubles. Henceforth, Kinetic energy is transformed into other forms of energy and vice versa. Let’s consider a few examples; a generator can convert K.E into electrical energy. The car brakes convert K.E to thermal energy. An internal combustion engine, steam turbine, and electric motor convert chemical, thermal, and electric energy into K.E.

## Types of Kinetic Energy

Types of Kinetic energy are:

### Radient Energy

The energy that travels by waves or particles is referred to as Radiant Energy. Electromagnetic waves create this energy, and we humans usually experience it in the form of heat. Some of the examples of radiant energy are:

- When an incandescent light bulb turns on, it emits heat as well as light. Both of these are forms of radiant energy.
- Another example of radiant energy is X-ray because it generates electromagnetic waves.
- The electric toaster has warmer heating components and emits radiant energy for toasting and heating the bread.
- Radio signals are another typical example.
- The Sun is the primary source of radiant energy.

### Thermal Energy

Both thermal and radiant energy are similar in terms of the way they are felt, i-e warmth. Radiant energy refers to waves or particles, while thermal energy shows the activity level among atoms or molecules in a matter. When they move quickly, they will collide more frequently. Due to this motion, thermal energy is categorized as kinetic energy. Some examples of thermal energy are as under:

- Geothermal energy, a renewable source of energy, is one example of thermal energy. Its primary source is decaying natural minerals and volcanic action of the earth.
- Baking in the oven or warming up food in a microwave also produces thermal energy.
- Geysers also produce thermal energy.
- When a vehicle or machine starts, the warmth produced in the engine is thermal energy.

### Sound Energy

Humans experience sound through vibrations. The sound source generates waves that travel through a medium like air and then reach our eardrums, then travel to the brain, and our brain interprets them as sound. A few examples of sound energy are hereunder:

- when we place our finger on the throat while speaking, we feel vibrations. Hence speaking is an excellent example of sound energy.
- Other examples include stereo speakers, a buzzing bee, drums, stamping your feet, etc.

### Electrical Energy

The flow of negatively charged electrons around the circuit produces electricity, also known as electrical energy. Some typical examples of electrical energy are:

- The fast discharge of electrons due to static electricity in clouds results in a lightning strike. Hence, lightning is a typical example of electrical energy.
- Connecting the positive and negative terminals of the battery with a lightbulb will create a simple circuit. We witness the power of electrical energy when the lightbulb illuminates.
- Other examples include electrical eels, AC/DC devices, etc.

### Mechanical Energy

Mechanical energy is one of the most prominent types of kinetic energy. It’s the energy concerned with the mechanical movement of bodies. The examples are stated below:

- Windmills capture wind energy due to the natural movement of air. This energy is further utilized to spin a turbine and produce electricity.
- Another example is the flowing river.
- A bullet fired from a gun.
- The bowling ball is another example of mechanical energy that is heading down the lane.
- When a person plays piano, the fingers are moving, which is an example of mechanical energy. They strike the keys of the piano, and energy is transferred, and finally, the hammer strikes the strings, resulting in sound energy.
- Kinetic energy enables us to move.

### Nuclear Energy

Nuclear energy is released from the core of atoms known as the nucleus, constituting protons and neutrons. This energy is produced through the fission (splitting atoms’ nuclei into many parts) or fusion (fusion of nuclei together). Some examples are discussed below:

- The nucleus of an atom of uranium-235 splits into two or three neutrons, barium nucleus, and krypton nucleus when a neutron hits it. It is an example of nuclear fission. Every time the reaction takes place, energy is released in the form of radiation and heat. A nuclear power plant is utilized to convert heat into electricity.
- The formation of helium when hydrogen nuclei fuse in stars is an example of nuclear fusion, producing nuclear energy.

## Forms of Kinetic Energy

Kinetic energy exists in different forms. They are:

#### Translation Kinetic Energy

When objects collide with one another, translational kinetic energy is produced. The significant concept concerning this energy is that all molecules of things travel in the same direction under the same applied force. The energy depends on motion through space. A typical example of translational kinetic energy is a golf club hitting a golf ball.

#### Vibrational Kinetic Energy

Vibrational kinetic energy is produced by objects when in vibration. It is an energy form possessed by bodies due to their vibrational motion. A vibrating smartphone and sound generated by drum solo are few among many examples.

#### Rotational Kinetic Energy

Bodies moving around an axis produce rotational kinetic energy. This energy depends on the body’s mass, how fast it is spinning around the axis, and the location of the center of mass concerning the axis. Examples of rotational kinetic energy in different objects include flywheels, turbines, Planet Earth, molecules (thermal kinetic energy), etc.

## Advantages of Kinetci Energy

The advantages of kinetic energy are stated below:

- Kinetic energy is abundant energy.
- The most prominent benefit of this energy is its capability to produce renewable energy.
- It can be harnessed and produce energy, for instance, hydroelectric, thermal, and wind power.
- Kinetic energy harnessing is used to maintain and build machines that ensure movement to effectively produce work, such as windmills, solar panels, hydroelectric turbines, etc.

## Disadvantages of Kinetci Energy

- Keeping kinetic energy at constant movement is pretty challenging.
- Friction hinders movement; therefore, it acts as an enemy to kinetic energy.
- We cannot always rely on kinetic energy. For instance, the wind doesn’t always blow, water isn’t always flowing, and shine may not shine daily. Therefore, we need intermediate energy sources.
- More space would be needed for machines harnessing kinetic energy in greater amounts. Those machines must also be substantial.
- It’s expensive to harness kinetic energy.
- Controlling friction can be challenging.

## Conclusion

All bodies in motion possess kinetic energy. The SI unit for K.E is Joule “J.” K.E exists in three different forms that are vibrational, rotational, and translational kinetic energy. Similarly, the types of Kinetic energy constitute electrical, thermal, mechanical, sound, nuclear, and radiant energy.

The equation of kinetic energy is ½ mv^{2} which shows its dependency on the velocity and mass of the object. The quantity only has magnitude and no direction; therefore, it is a scalar quantity. The blog intends to give an in-depth explanation on derivation for the equation of K.E, advantages, disadvantages, examples, and some laws applicable to the quantity.