What could these four photos possibly have in common? Can you guess what it is? All of them show things that have kinetic energy.

### Defining Kinetic Energy

**Kinetic energy** is the energy of moving matter. Anything that is moving has kinetic energy—from atoms in matter to stars in outer space. Things with kinetic energy can do work. For example, the spinning saw blade in the photo above is doing the work of cutting through a piece of metal.

### Calculating Kinetic Energy

The amount of kinetic energy in a moving object depends directly on its mass and velocity. An object with greater mass or greater velocity has more kinetic energy. You can calculate the kinetic energy of a moving object with this equation:

\begin{align*}\mathrm{Kinetic\; Energy\; (KE)=\frac{1}{2} mass \times velocity^2}\end{align*}

This equation shows that an increase in velocity increases kinetic energy more than an increase in mass. If mass doubles, kinetic energy doubles as well, but if velocity doubles, kinetic energy increases by a factor of four. That’s because velocity is squared in the equation.

Let’s consider an example. The **Figure** below shows Juan running on the beach with his dad. Juan has a mass of 40 kg and is running at a velocity of 1 m/s. How much kinetic energy does he have? Substitute these values for mass and velocity into the equation for kinetic energy:

\begin{align*}\text{KE}=\frac{1}{2} \times 40 \ \text{kg} \times (1\frac{\text{m}}{\text{s}})^2=20 \ \text{kg} \times \frac{\text{m}^2}{\text{s}^2}=20 \ \text{N} \cdot \text{m},\end{align*} or \begin{align*}20 \ \text{J}\end{align*}

Notice that the answer is given in joules (J), or N • m, which is the SI unit for energy. One joule is the amount of energy needed to apply a force of 1 Newton over a distance of 1 meter.

What about Juan’s dad? His mass 80 kg, and he’s running at the same velocity as Juan (1 m/s). Because his mass is twice as great as Juan’s, his kinetic energy is twice as great:

\begin{align*}\text{KE}=\frac{1}{2} \times 80 \ \text{kg} \times (1 \frac{\text{m}}{\text{s}})^2=40 \ \text{kg} \times \frac{\text{m}^2}{\text{s}^2}=40 \ \text{N} \cdot \text{m}\end{align*}, or \begin{align*}40 \ \text{J}\end{align*}

**Q:** What is Juan’s kinetic energy if he speeds up to 2 m/s from 1 m/s?

**A:** By doubling his velocity, Juan increases his kinetic energy by a factor of four:

\begin{align*}\text{KE}=\frac{1}{2} \times 40 \ \text{kg} \times (2 \frac{\text{m}}{\text{s}})^2=80 \ \text{kg} \times \frac{\text{m}^2}{\text{s}^2}=80 \ \text{N} \cdot \text{m}\end{align*}, or \begin{align*}80 \ \text{J}\end{align*}

Review how kinetic energy is related to mass and velocity by watching this cartoon: http://www.schooltube.com/video/faddf7cb14ade293baad/

### Summary

- Kinetic energy (KE) is the energy of moving matter. Anything that is moving has kinetic energy.
- The amount of kinetic energy in a moving object depends directly on its mass and velocity. It can be calculated with the equation: \begin{align*}\text{KE}=\frac{1}{2}\text{mass} \times \text{velocity}^2\end{align*}.

### Explore More

At the following URL, review kinetic energy and how to calculate it. Then take the quiz at the bottom of the Web page. Be sure to check your answer. http://www.physicsclassroom.com/class/energy/u5l1c.cfm

### Review

- What is kinetic energy?
- The kinetic energy of a moving object depends on its mass and its
- volume.
- velocity.
- distance.
- acceleration.

- The bowling ball in the
**Figure**below is whizzing down the bowling lane at 4 m/s. If the mass of the bowling ball is 7 kg, what is its kinetic energy?