Energy⏱ 4 min read

Kinetic Energy

KE = ½mv²

What is the Kinetic Energy?

Kinetic energy is the energy an object possesses because it's moving. Any moving object — a rolling ball, a flying plane, a speeding car — has kinetic energy, and the faster it moves or the more massive it is, the greater that energy.

Because velocity is squared in the formula, kinetic energy grows much faster than speed does: doubling an object's speed quadruples its kinetic energy, and tripling its speed makes it nine times greater. This is exactly why high-speed collisions are so disproportionately more dangerous than low-speed ones.

What Each Variable Means

Kinetic energyThe energy of motion. (joules (J))

MassThe amount of matter in the moving object. (kilograms (kg))

VelocityThe speed of the object. Because it's squared, doubling speed quadruples KE. (m/s)

When to Use It

Calculating the energy of a moving object from its mass and speed
Comparing the destructive potential of objects moving at different speeds
As one term in the work-energy theorem, relating work done to change in kinetic energy

Step-by-Step Example

Problem: A 2 kg ball rolls at 5 m/s. What is its kinetic energy?

Identify the known values

Mass and velocity are both given.

m = 2 kg, v = 5 m/s

Square the velocity first

Compute v² before multiplying.

v² = 5² = 25 m²/s²

Substitute and calculate

Multiply by ½ and the mass.

KE = 0.5 × 2 × 25 = 25

✓

Answer: KE = 25 J

Interactive Calculator

m (mass) (kg)v (velocity) (m/s)

Result will appear here

Common Mistakes

Mistake: Forgetting to square the velocity.
Fix: KE = ½mv² squares v, not m — a very common slip that gives an answer far too small at higher speeds.
Mistake: Forgetting the factor of ½.
Fix: The ½ isn't optional — dropping it doubles every kinetic energy calculation.

Practice Questions

A 4 kg object moves at 3 m/s. Find its kinetic energy.
If an object's speed doubles, what happens to its kinetic energy?

Frequently Asked Questions

Why does doubling speed quadruple kinetic energy?

Because velocity is squared in the formula — (2v)² = 4v², so doubling v multiplies the KE term by 4, not 2.

What's the difference between kinetic and potential energy?

Kinetic energy is the energy of motion; potential energy is stored energy due to position (like height above the ground). Many physics problems involve energy converting between the two.