Potential and kinetic energy are the two major types of energy. Here is a look at kinetic energy, including its definition, examples, units, formula, and how to calculate it.

### Kinetic Energy Definition

In physics, kinetic energy is the energy an object has due to its motion. It is defined as the work required to accelerate a body of a given mass from rest to a certain velocity. Once the mass reaches the velocity, its kinetic energy remains unchanged unless its speed changes. However, velocity and thus kinetic energy depend on the frame of reference. In other words, an object’s kinetic energy is not invariant.

### Kinetic Energy Units

The SI unit of kinetic energy is the joule (J), which is a kg⋅m^{2}⋅s^{−2}. The English unit of kinetic energy is the foot-pound (ft⋅lb). Kinetic energy is a scalar quantity. It has magnitude, but no direction.

### Kinetic Energy Examples

Anything you can think of that has mass (or apparent mass) and motion is an example of kinetic energy. Kinetic energy examples include:

- A flying aircraft, bird, or superhero
- Walking, jogging, bicycling, swimming, dancing, or running
- Falling down or dropping an object
- Throwing a ball
- Driving a car
- Playing with a yo-yo
- Launching a rocket
- A windmill spinning
- Clouds moving across the sky
- The wind
- An avalanche
- A waterfall or flowing stream
- Electricity flowing through a wire
- Orbiting satellites
- A meteor falling to Earth
- Sound moving from a speaker to your ears
- Electrons orbiting the atomic nucleus
- Light traveling from the Sun to the Earth (photons have momentum, so they have apparent mass)

### Kinetic Energy Formula

The formula for kinetic energy (KE) relates energy to mass (m) and velocity (v).

KE = 1/2 mv^{2}

Because mass is always a positive value and the square of any value is a positive number, kinetic energy is always positive. Also, this means the maximum kinetic energy occurs when velocity is greatest, regardless of the direction of motion.

From the kinetic energy equation, you can see an object’s velocity matters more than its mass. So, even a small object has a lot of kinetic energy if it’s moving quickly.

The kinetic energy formula works in classical physics, but it starts to deviate from true energy when the velocity approaches the speed of light (*c*).

### How to Calculate Kinetic Energy

The key to solving kinetic energy problems is to remember that 1 joule equals 1 kg⋅m^{2}⋅s^{−2}. Speed is the magnitude of velocity, so you can use it in the kinetic energy equation. Otherwise, watch your units in fractions. For example, (1)/(400 m^{2}/s^{2}) is the same as (1/400) s^{2}/m^{2}.

#### Example #1

Calculate the kinetic energy of a 68 kg person moving with a speed of 1.4 m/s (in other words, the kinetic energy of a typical person walking).

KE = 1/2 mv^{2}

Plugging in the numbers:

KE = 1/2(68 kg)(1.4 m/s)^{2}

KE = 66.64 kg⋅m^{2}⋅s^{−2}

KE = 66.64 J

#### Example #2

Calculate the mass of an object moving at 20 m/s with a kinetic energy of 1000 J.

Rearrange the kinetic energy equation to solve for mass:

m = 2KE/v^{2}

m = (2)(1000 kg⋅m^{2}⋅s^{−2})/(20 m/s)^{2}

m= (2000 kg⋅m^{2}⋅s^{−2})/(400 m^{2}/s^{2})

m = 5 kg

### Difference Between Kinetic and Potential Energy

Kinetic energy can transform into potential energy, and vice versa. Kinetic energy is the energy associated with a body’s motion, while potential energy is the energy due to an object’s position. All the other types of energy (e.g., electrical energy, chemical energy, thermal energy, nuclear energy) have kinetic energy, potential energy, or a combination of the two. The sum of the kinetic and potential energy of a system (its total energy) is a constant because of Conservation of Energy. In quantum mechanics, the sum of kinetic and potential energy is called the Hamiltonian.

A frictionless roller coaster is a good example of the interplay between kinetic and potential energy. At the top of the track, the roller coaster has maximum potential energy, but minimum kinetic energy (zero). As the cart goes down the track, its velocity increases. At the bottom of the track, the potential energy is at its minimum (zero), while the kinetic energy is at its maximum.

### References

- Goel, V. K. (2007).
*Fundamentals Of Physics*. Tata McGraw-Hill Education. ISBN 978-0-07-062060-5. - Serway, Raymond A.; Jewett, John W. (2004).
*Physics for Scientists and Engineers*(6th ed.). Brooks/Cole. ISBN 0-534-40842-7. - Tipler, Paul; Llewellyn, Ralph (2002).
*Modern Physics*(4th ed.). W. H. Freeman. ISBN 0-7167-4345-0.