What is kinetic energy?

When an object is in motion, it is capable of doing work. We say that the object has kinetic energy (KE) or energy of motion. Does it make sense to you that the object is capable of doing work? Take a look at the carts below.

The cart on the left is pushing the cart on the right and thus doing work on it or applying a force over a certain distance. The cart on the left has KE or energy of motion.

Kinetic energy

kinetic energy formula

Suppose an object has mass m and is moving with a speed v, we define kinetic energy (KE) as

KE =
1 / 2

The unit for the mass or m is kg, the unit for the speed or v is m/s, and the unit for the kinetic energy or KE is joules.

Derivation of kinetic energy formula

To derive the formula, we will need a few concepts.

  •    We will need the work formula.
Therefore, the 3 equations we need are

F = ma      equation 1

v2 = v02 + 2ad     equation 2

W = Fd     equation 3

We will combine these 3 equations, do some math, and finally arrive at the formula for kinetic energy.

We will start with W = Fd since what we are looking is the work a moving object can do.

W = F × d

Using equation 3, substitute ma for F

W = ma × d      equation 4

Now, use equation 2 to solve for a

v2 = v02 + 2ad

v02 + 2ad = v2

Let v0 = 0. Why? Since the object is usually at rest before starting moving, the initial speed will be zero then.

02 + 2ad = v2

0 + 2ad = v2

2ad = v2

Divide both sides by 2d

a =
v2 / 2d

Replace the value of a in equation 4

W = m
v2 / 2d

W = m
v2 / 2

Substitute KE for W since the work done by a moving object is called KE or kinetic energy.
KE = m
v2 / 2

KE =
mv2 / 2

An important observation about the kinetic energy

Notice that the speed is squared. What happens if we double the speed?

Let v be the speed of a moving object. Let speed =  2v after the speed is doubled. 

KE = m
(2v)2 / 2

KE = m
4v2 / 2

KE = 4
mv2 / 2

The 4 that you see means that the kinetic energy is quadrupled.

Whenever the speed is doubled, the kinetic energy is quadrupled.

This is an interesting finding. Here is what it means in terms of driving a vehicle. If you go from 40 miles per hour to 80 miles per hour, it will take four times as much work to stop the vehicle.

Recent Articles

  1. Calculate the Conditional Probability using a Contingency Table

    Mar 29, 23 10:19 AM

    Contingency table
    Learn to calculate the conditional probability using a contingency table. This contingency table can help you understand quickly and painlessly.

    Read More

  2. Rational Numbers - Definition and Examples

    Mar 15, 23 07:45 AM

    Rational numbers
    To learn about rational numbers, write their decimal expansion, and recognize rational numbers that are repeating decimals and terminating decimals.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes


Math vocabulary quizzes