## What Is Kinetic Energy?

Kinetic energy is defined as the energy of motion. As a type of energy, it can be conserved. However, in many situations, it is transformed into heat and/or sound. Kinetic energy is often paired with potential energy, as potential energy can be defined as the energy stored prior to motion taking place. Since energy is conserved and takes different forms, it is common for kinetic energy to be paired with potential energy, as both are easily measurable quantities. To see instances of only kinetic energy being conserved, using collisions as an example may be fruitful. This is because elastic collisions are those that conserve the motion of all bodies before and after collision.

Since kinetic energy deals with motion, it can be represented by any of the classical Newtonian Laws of Motion, such as force (through acceleration’s relationship with velocity) or momentum.

The unit of kinetic energy is the joule, which is equal to one kilogram-squared meter per squared second (1 kg m^{2}/s^{2}). If an object is not moving, its kinetic energy is zero.

## Derivations of Kinetic Energy

Since kinetic energy is the motion of energy, many different types of energy can be derived from it. To understand why, we must understand that all motion begins at the atomic level.

The objective of any atom is to reach its lowest energy level. This comes about if they fill their outermost shell, also called the *valence shell*, with the requisite number of electrons. If there are no electrons for the atoms to take, however, they will naturally be at a higher energy level. Regardless of if electrons are around, the atom will still do what it can to release as much energy as possible. One of the actions it takes is vibration. The more energy that is within any given atom, the faster that atom will vibrate. When atoms vibrate, they release multiple types of energy.

One of them is heat, or thermal energy. You’ve probably noticed its presence when you shiver in the cold. The shivering is actually caused by your muscles rapidly shaking to create heat. In other words, the motion of your muscles generates heat; yet another example of the transition between kinetic and thermal energy.

Another transition is between motion and sound. The sounds that reach your ear are the result of vibrations in molecules with the air. As such, sound is a unique kind of energy that requires the existence of molecules to travel. This is why, in the vacuum of space, you can’t hear anything.

It is important to note that vibration occurs in any state of matter. It’s easy to understand the movement of gaseous atoms. After all, these atoms are unbonded and freely moving. However, even the sturdiest solids are moving at the microscopic level.

## Kinetic Energy Formula

The kinetic energy is dependent on motion. Therefore, it must take the mass of the object and its velocity into consideration. Experimentally, scientists have determined that any moving object follows the following formula:

$K=\frac{m{v}^{2}}{2}$where is mass and is velocity. Since the velocity is squared in this equation, a small change on velocity can lead to a massive change. For example, doubling the velocity quadruples its energy. Furthermore, it is impossible for kinetic energy to be negative, given the squared velocity. Conceptually, this means that it doesn’t matter what direction something is moving in. In the case where all of the variables are the same, the kinetic energy will also remain the same. That is not to say that direction doesn’t matter; velocity is a vector term, meaning that it carries with it a magnitude and direction.

## Kinetic Energy Examples

Kinetic energy is most easily conceptualized in moving objects that you can see.

- A 100 kilogram (kg) car is moving at a speed of 25 meters per second (m/s). What is the kinetic energy of the car?
- Plug in all of the terms into the kinetic energy formula:
- $K=\frac{m{v}^{2}}{2}$
- $\frac{100kg*(25m/s{)}^{2}}{2}=\frac{62,500kg{m}^{2}/{s}^{2}}{2}=31,250J$

Remember, momentum, the product of mass and velocity (*mv*), contains velocity as a term too. If given the momentum and the mass, you can find out the mass’ kinetic energy as well. For example:

The momentum of an Olympic track runner was measured to be 600 kg m/s. Her mass is 60 kg. Determine the kinetic energy that they moved with.

- We already have the mass from the given material. All we need now is the velocity, which we can find through the momentum.
- $P=mv$
- $600kgm/s=60kg*v$
- $v=\frac{600kgm/s}{60kg}$
- $v=10m/s$

- Kinetic Energy can then be solved by plugging this velocity into the equation.
- $K=\frac{m{v}^{2}}{2}=\frac{60kg*(10m/s{)}^{2}}{2}=3000J$

## Quiz