Kinetic Energy
Simple Explanation
Kinetic energy is the energy an object has because it is moving: KE = ½mv². Because speed is SQUARED in this formula, doubling an object's speed doesn't just double its kinetic energy — it QUADRUPLES it.
Why Do We Need It?
This squared relationship is exactly why high-speed crashes are so much more dangerous than low-speed ones — a car going twice as fast carries four times the kinetic energy that must be absorbed in a collision.
Formula
Kinetic Energy
KE = ½mv²
Kinetic energy is the energy an object has because it is moving. It grows with the SQUARE of speed, so doubling the speed of an object quadruples its kinetic energy.
- KE
- — kinetic energy, in joules (J)
- m
- — mass of the object, in kilograms (kg)
- v
- — speed of the object, in metres per second (m/s)
When to use it: Whenever the energy of a moving object needs to be found from its mass and speed.
Worked Example
Find a car's kinetic energy
A 1000 kg car travels at 20 m/s. Find its kinetic energy.
Why Does This Work?
The squared dependence on speed comes directly from how kinetic energy is built up: bringing an object up to speed v from rest requires work that itself scales with v² — a consequence of combining Newton's second law with the equations of motion.
Real-Life Example
Why speed limits matter so much for safety
A speed limit reduction from 60 km/h to 30 km/h (halving the speed) is often used near schools.
Because kinetic energy depends on the square of speed, halving the speed cuts the kinetic energy involved in any collision to just a QUARTER — a far bigger safety improvement than the halved speed alone suggests.
Practice
Find the kinetic energy of a 2 kg ball moving at 6 m/s.
MediumAn object's speed is tripled. By what factor does its kinetic energy change?
MediumCommon mistake
Forgetting to square the velocity — a very common algebra slip that gives an answer far too small; always square v BEFORE multiplying by ½m.
Quick Review
- KE = ½mv²
- Kinetic energy depends on the SQUARE of speed — doubling speed quadruples KE.
- This is why high-speed collisions are disproportionately dangerous.