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Kinetic Energy
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ℹ️ KE = ½mv² applies to classical (non-relativistic) mechanics. For objects moving at speeds above ~10% of the speed of light, relativistic kinetic energy formula must be used.
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Sources & Methodology
Kinetic energy formula per classical mechanics; per Serway & Jewett Physics for Scientists and Engineers and NIST.
Serway & Jewett — Physics for Scientists and Engineers, 10th Ed.
Standard university physics reference for kinetic energy, work-energy theorem, and energy unit conversions.
NIST — Fundamental Physical Constants
Energy conversion factors and SI unit definitions. physics.nist.gov
IUPAC — SI Units and Physical Quantities in Chemistry
Joule definition, energy unit conversion factors, and SI conventions for energy calculations.
KE = (1/2) x m x v^2 [SI: m in kg, v in m/s, KE in joules]
v = sqrt(2 x KE / m)
m = 2 x KE / v^2
1 J = 1 kg·m²/s²
v = sqrt(2 x KE / m)
m = 2 x KE / v^2
1 J = 1 kg·m²/s²
KE = ½ × m × v²
Example: 2 kg ball moving at 10 m/s.
KE = 0.5 × 2 × 10² = 0.5 × 2 × 100 = 100 J
Double the speed: KE = 0.5 × 2 × 20² = 400 J (4x more energy)
KE = 0.5 × 2 × 10² = 0.5 × 2 × 100 = 100 J
Double the speed: KE = 0.5 × 2 × 20² = 400 J (4x more energy)
Last reviewed: April 2026
How Is Kinetic Energy Calculated?
Kinetic energy (KE) is the energy an object possesses due to its motion. The formula KE = ½mv² shows that kinetic energy depends on both mass and the square of velocity. The quadratic relationship with velocity has important real-world implications: doubling speed quadruples kinetic energy, which is why high-speed crashes are dramatically more destructive than low-speed ones.
The SI unit of energy is the joule (J), defined as 1 kg·m²/s². One joule is the kinetic energy of a 2 kg object moving at 1 m/s. For context, a 1500 kg car at 60 km/h (16.67 m/s) has about 208,000 joules — the same energy as detonating about 50 grams of TNT.
Kinetic Energy at Different Speeds — 1500 kg Car
| Speed | m/s | Kinetic Energy | Notes |
|---|---|---|---|
| 30 km/h | 8.33 | 52,083 J | City speed limit |
| 60 km/h | 16.67 | 208,333 J | 4x more than 30 km/h |
| 100 km/h | 27.78 | 578,704 J | 11x more than 30 km/h |
| 120 km/h | 33.33 | 833,333 J | 16x more than 30 km/h |
💡 Work-Energy Theorem: Net work done on an object equals its change in kinetic energy: W = ΔKE = KE_final − KE_initial. To stop a car moving at 100 km/h, the brakes must do −578,704 J of work. At 60 km/h, only −208,333 J is needed. This is why stopping distance increases with the square of speed, not linearly.
Frequently Asked Questions
KE = ½mv². m = mass in kg, v = velocity in m/s, KE = kinetic energy in joules (J). KE is always positive and increases with the square of velocity.
KE = 0.5 × m × v². Example: 2 kg at 10 m/s: KE = 0.5 × 2 × 100 = 100 J. Double speed: KE = 0.5 × 2 × 400 = 400 J (4× more).
Joules (J) in SI. 1 J = 1 kg·m²/s². Also: kJ, cal, kcal, eV, BTU. The calculator converts between all of these.
KE ∝ v². Doubling speed = 4× KE. Tripling speed = 9× KE. This is why car crash severity increases much faster than speed increases.
KE ∝ m. Doubling mass doubles KE (at same speed). A 2000 kg truck has twice the KE of a 1000 kg car at the same velocity.
KE = energy of motion (½mv²). PE = stored energy of position (mgh for gravity). They convert: a falling object converts PE to KE; a rising object converts KE to PE. Total mechanical energy is conserved (no friction).
W = ΔKE = KE_final − KE_initial. Net work done on an object equals the change in its kinetic energy. Used to calculate braking distance, acceleration work, and impact energy.
v = sqrt(2 × KE / m). Example: 200 J, 4 kg: v = sqrt(400/4) = sqrt(100) = 10 m/s.
Temperature is proportional to average molecular KE: KE_avg = (3/2)kT where k = Boltzmann constant, T = temperature in Kelvin. At 25°C (298 K), average KE per molecule = 6.17 × 10−²¹ J.
KE = (γ − 1)mc² where γ = 1/sqrt(1−v²/c²). The classical ½mv² breaks down above ~10% of the speed of light. At 50% of c, classical formula underestimates KE by about 8%.
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