**History and Etymology of Kinetic Energy**

The word kinetic is an adjective that means motion. The principle E ∝ mv² was developed by Johann Bernoulli and Gottfried Leibniz who labelled kinetic energy as a living force. An experimental evidence was provided by Willem s’ Gravesande from Netherlands. The square of impact speed is proportional to the penetration depth and it was determined by allowing weights to drop into block of mud from different altitudes. The implications of the said experiment were recognized by Émilie du Châtelet and an explanation was published. The current scientific meanings of work and kinetic energy were from the mid-19th century. The early understandings of the ideas are credited to Gaspar-Gustave Coriolis who published Du Calcul de l'Effet des Machines in 1829 that outlines the math of the kinetic energy. The credit was given to William Thompson for creating the phrase kinetic energy.

**How it Works**

Moving objects such as a roller coaster have KE or kinetic energy. For example, if a car running at 5 mph crashes in the wall, the car will not be damaged that much but if the car is running for 40 mph, it will be damaged totally. The more weight the object has, the faster it will move and the more kinetic energy the object will have. Kinetic energy is the needed work to accelerate a certain object with a given mass at rest to its specified velocity. The object maintains its kinetic energy until it changes its speed. Similar amount of work is needed by an object to decelerate from its present speed until rest and accelerate from rest to its present speed. Kinetic energy is similar to potential energy. It is the energy that an object has from its position. This is in harmony with the law of conservation of energy that states that energy cannot be created nor destroyed; it can only be transformed from one form to another.

**General Relativity**

The well-known Einstein formula for energy is: E= mc2 This includes both the rest mass energy and kinetic energy of a particle. The kinetic energy of a particle moving in high speed can be calculated from: KE= mc2 – m0c2 General relativity is the gravitation’s geometric theory that was published by Albert Einstein in 1916. In modern physics, general relativity is the approved representation of gravitation. The general theory of relativity generalizes Newton’s Law of Universal Gravitation and special relativity which provide a unified presentation of the gravitational force as geometric property of time and space. Compared to the classical physics, this theory by Einstein has significant differences when it comes to the predictions which concern time’s passage space geometry, motion of objects that are falling freely and light propagation. To date, all of the predictions related to general relativity are confirmed in experiments and observations. Although this theory is not the only one related, it is the simplest theory which is consistent to any experimental data. With the discovery of kinetic energy, the world has become a better place to live in with all these inventions that are discovered through the help of the kinetic power.

**Derivation Kinetic**

energy is linked closely to the displacement vector over the applied force and work concept which is the dot product or scalar product of force. Using the basic equations of kinematics, an equation for object acceleration which changes the speed is obtained. In this equation, the term x-xo is replaced by s which represents the displacement total distance. v2 = v02 + 2as therefore, a = (v2 - v02 ) / 2s Applying the Newton’s Second Law of motion, since F=ma, you get F = ma = m (v2 - v02) / 2s and multiply the distance s for work then break it and you get: W = Fs = 0.5mv2 - 0.5mv02 The kinetic energy (KE) is defined as: K = 0.5mv2 It must be noted that this quantity will be a non-zero scalar quantity. If any object is moving and has mass, it will be positive always. If the object has no mass or at rest or zero velocity, the quantity is zero. Therefore, the equation of kinetic energy gives information about the speed but not the direction of an object’s motion.

**Kinetic Energy Formulas and Equations**

Solving for the kinetic energy of an object is easy using the formula K = 1/2 mv² Where K = kinetic energy, m = mass, v = velocity Mass of the object is expressed in kilograms while the velocity is expressed in meter per second. If you want to solve for the different unknowns, you can use the following equations: m = 2K/v² in solving for mass and v = to the square root of 2K over m in solving for the velocity In physics, energy is among vaguest concepts to understand because it takes different forms and all things that occur in the world is one of the major or subtle energy change. In calculating the energy on its every form, there is a formula and there are 2 mechanic forms. One is the relativistic mechanics and the second is the Newtonian mechanics. Out of the two, relativistic is the most accurate compared to Newtonian mechanics and is only applicable if the object’s velocities are lesser than light speed.

**Rigid Body or Point Mass Formula**

The following is the kinetic energy formula of a rigid body or point mass moving at a speed which is less than the speed of the light or non-relativistic speeds. Kinetic Energy (KE) = ½ X M V2 Where m is equal to the mass of a rigid body or point mass and v is equal to the velocity in which an object is moving. Joule is the unit of energy. The formula above can be expressed also in momentum like: Kinetic Energy = P2 / 2M Where, M is the mass and P is equal to the momentum of an object.

**Rotational KE**

The basic kinetic energy formula above is not applicable if instead of an object moving in liner motion it is rotating. The rotating formula for objects is the following: Rotational Kinetic Energy = ½ X I X ω2 Where, I is the moment of inertia of an object while ω is the angular velocity. To get the kinetic energy of an object, the angular velocity and the moment of inertia should be calculated.

**Relativistic Kinetic Energy**

Kinetic energy formula that is based from the Newtonian mechanics is not applicable if dealing with the relativistic energy. The relativistic energy formula is: KErelativistic = m γ c2 - mc2 where, γ = 1/(√(1-v2/ c2), m is the mass of an object, c is the velocity of light, v is the velocity of an object based on the reference frame.

**Applications of Kinetic Energy**

Kinetic energy is an important portion of energy which is among physics’ central themes. It is very important for you to know about kinetic energy and how this power works. The theorem of work energy is among the most vital applications of kinetic energy in physics. The theorem describes the change of energy in an object to the force that causes it, meaning that determining on how an object will behave when energy is applied is possible. Not all people will realize the work energy theorem entirely, so an example is necessary. A good case for this is a car that moves at a known velocity. If you the brakes’ force, you can measure the distance that the vehicle will cover before it stops after you applied the brakes. It is necessary to know that it doesn’t matter what type of motion happens. Whether translational, oscillatory or any type of motion; all of them have kinetic energy which means that all objects that move contains kinetic energy which can be accumulated and transformed into other kinds of useful energy. There are factors that help in determining the energy that an object contains and one of this is the velocity of the object on the move and the other is its actual mass. Kinetic energy is very useful to humans due to the many benefits that it provides. Hydroelectric dams are the ones that provide electricity all around the world. This is made possible due to the large quantity of energy that the moving water contains. These water reservoirs are developed to increase the mass of the water and as the water falls from the dams, it increases its speed. When these two variables are increased, the amount of kinetic energy is also increased. The water from these dams is then transformed to become electricity once it undergoes several complicated processes. Other things that make use of kinetic energy include those appliances that are powered by pedals such as lawn mowers, snowplows and washing machines. There are a lot of applications of kinetic energy which has made the world a fabulous place to live in. Nowadays, there are still new discoveries about the applications of kinetic energy all around the world which are very useful to humans.

**Kinetic Theory**

Kinetic theory is a theory concerning the nature of gas. This theory has many names such as kinetic-molecular theory, kinetic theory of gasses and collision theory. It assumes that the molecules of the gas are perfectly elastic and spherical and that the collisions in the container walls are elastic as well. This means that there is no change in velocity. The gas molecules total volume is negligible compared to the containers total volume. It means that there is plenty of space between the gas molecules. The only factor that affects the kinetic energy average is the temperature of the gas molecules.