Kinetic energy is a form of energy that **occurs when an object, substance or particle is in motion**. This energy **depends** mostly **of speed** of the object, in addition to its **mass**. For example, when we run, our body is in motion, so it produces kinetic energy.

Kinetic energy is usually abbreviated with the letters “Ec” or “Ek”, and can be expressed with the following formula:

Below we explain each term and the units used according to the International System:

**Ec**: is the kinetic energy measured in Joules or Joules, **J.**.

**m**: is the mass of the body in motion, measured in kilograms, **kg**.

**v**: is the speed of the body, measured in meters per second, **m/s**. Since this term is squared (**v2**), the final units are **m2/s2**.The equation is divided by **2**since the kinetic energy formula is the result of deriving and integrating the formula of Newton’s Second Law (Force = Mass · Acceleration) into the work formula (Work = Force · Displacement).

Kinetic energy is linked to other physics concepts such as work and force. The object, being in motion, causes a specific work and force. For example, if the kinetic energy creates enough force, the object can deform or displace another.

An object in motion can return to its initial state or reach a state of rest if another force acts on it. The work caused by the external force counteracts that of the kinetic energy of the object. For example, a wheel that goes down a slope until it hits a wall. The wall applies a greater force on the wheel, so it will stop moving, reducing its kinetic energy to zero.

Likewise, an object generates kinetic and/or potential energy. When the object is at rest, the kinetic energy is zero, while the potential energy is maximum. If the object is in motion and there are no other forces acting on it, it generates kinetic energy, but not potential energy. Finally, an object moving within a gravitational field always generates kinetic and potential energy.

## Types of kinetic energy and examples

There are three types of kinetic energy: translation, rotation and vibration.

The **translational kinetic energy** It occurs when an object moves from one point to another. When moving in one direction, the acceleration applied to the mass of the object is translated into kinetic energy. Some examples are the action of walking, driving a vehicle on the highway, or falling objects.

The **rotation kinetic energy** It occurs when an object rotates on itself. Although there is no displacement, part of the object accelerates around an axis, generating kinetic energy. Examples of this are the movement of records in players, the yo-yo, and the movement of windmill blades due to the wind.

The **vibration kinetic energy** It occurs when particles oscillate around an equilibrium point. Some examples are the vibration of the mobile phone, the movement of the strings of a guitar or molecular vibration.

In addition, kinetic energy can be represented in other types depending on the effect or type of energy they generate. These are:

**Mechanical energy**: the movement of objects and their physical interaction with others produces mechanical movement, the result of kinetic and potential energy. An example of this is when we hit a ball. The kinetic energy of our foot is transferred to the ball, producing mechanical energy in the form of displacement.

**Thermal energy**: The vibration and movement of the particles of a substance releases heat, that is, thermal energy. Depending on the state of aggregation of the matter (solid, liquid or gas), the thermal energy will be greater or less.

**Electric power**: Electrons, when moving through an electrical circuit, generate electricity from their kinetic and potential energy.

**sound energy**: is a type of mechanical energy that results from the oscillation or vibration of particles in the form of waves. This oscillation generates sound waves that the ear can pick up.

## Examples of exercises using the kinetic energy formula

### Exercise 1

An object A of mass 58 kilograms is moving at 15 meters per second, while an object B of mass 20 kilograms is moving at 26 meters per second. Which of the two objects generates the greatest kinetic energy?

To find out, let’s first calculate the kinetic energy of object A:

Next, let’s calculate the kinetic energy of object B:

By comparing both figures, we can conclude that the **object B generates more kinetic energy than object A**. An object’s speed, when squared in the formula, has a greater impact on kinetic energy than mass.

### Exercise 2

Let’s imagine that a bowler throws a ball of mass 14 kilograms. When the ball collides with the pins or pins, a kinetic energy of 448 Joules is detected. How fast was the ball traveling before it collided?

If we replace the terms of the equation, we have:

If we solve for the velocity in the formula, we have:

Therefore, the ball moved to **8 meters per second** before colliding with the pins or pins. Remember that 1 Joule is equivalent to 1 (kg·m2)/s2.

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