What is kinetic energy?
The energy an object has because of its motion — half its mass times its velocity squared, measured in joules. A 1,500 kg car at 20 m/s carries 300,000 joules. Because it depends on velocity squared rather than velocity, speed matters far more than mass: doubling the speed quadruples the energy, while doubling the mass only doubles it.
Why is the velocity squared so important?
It is the single most consequential fact about road safety. A crash at 60 mph releases four times the energy of one at 30, not twice, because the energy scales with the square. It also explains stopping distances: braking must dissipate all that energy, so doubling speed roughly quadruples the distance needed. Intuition treats speed as linear, and it simply is not.
How does kinetic energy differ from momentum?
Momentum is mass times velocity; kinetic energy is half mass times velocity squared. Momentum is conserved in every collision, while kinetic energy is only conserved in elastic ones — the rest goes into deformation, heat and sound. Momentum tells you about the difficulty of stopping something; energy tells you about the damage it does when it stops suddenly.
Where does the energy go in a collision?
Into deforming metal, heating materials, breaking things and making noise. That is a feature, not a loss: crumple zones exist to convert kinetic energy into deformation over as long a distance as possible, reducing the peak force on occupants. A perfectly rigid car would conserve more energy and be far more dangerous, because the energy would go into the people instead.
What is the work-energy theorem?
The work done on an object equals its change in kinetic energy. Since work is force times distance, it follows that stopping distance and stopping force trade off: the same energy can be absorbed by a large force over a short distance or a small force over a long one. This is the reasoning behind run-off areas, safety nets, and why landing on concrete differs from landing on a mat.
Can kinetic energy be negative?
No. Mass is positive and velocity is squared, so kinetic energy is always zero or positive — unlike momentum, which carries a sign. A *change* in kinetic energy can be negative, meaning the object slowed. This is a useful sanity check: a negative kinetic energy in your working means an arithmetic error rather than a physical result.