Energy of motion
Every moving object carries kinetic energy, the energy it took to bring it up to speed and the energy it must lose to stop. It depends on mass and, above all, on speed:
KE = ½ × m × v², in joules when m is in kilograms and v in meters per second.
Because speed is squared, doubling the speed multiplies the energy by four. That is the physics behind stopping distances, crash severity and the destructive power of a hailstone.
Related quantities
- Momentum p = m × v, in kg·m/s. It decides how hard an object is to stop in a given time and is conserved in collisions.
- Equivalent fall height h = v² ÷ (2g): the height from which a free fall would produce the same speed, and therefore the same impact. It does not depend on mass.
- Units: 1 kJ = 1,000 J; 1 Wh = 3,600 J; 1 food calorie (kcal) = 4,184 J.
Worked example: a 3,300 lb car at 30 mph
- Convert: 3,300 lb = 1,497 kg and 30 mph = 13.41 m/s.
- KE = ½ × 1,497 × 13.41² = 134.6 kJ.
- Momentum: 1,497 × 13.41 = 20,075 kg·m/s.
- Equivalent fall height: 13.41² ÷ 19.61 = 9.2 m, about 30 feet, roughly a fall from a third-story window.
Energy at other speeds (same car)
| Speed | Kinetic energy | Equivalent fall |
|---|---|---|
| 10 mph | 15.0 kJ | 3.3 ft |
| 20 mph | 59.8 kJ | 13.4 ft |
| 30 mph | 134.6 kJ | 30 ft |
| 45 mph | 302.9 kJ | 68 ft |
| 55 mph | 452.4 kJ | 101 ft |
| 70 mph | 732.9 kJ | 164 ft |
Going from 30 to 45 mph, only 50% faster, more than doubles the energy that the brakes, or a crash, must absorb. At 70 mph, a car carries the energy of a fall from a 16-story building.
Everyday examples
| Object | Mass | Speed | Kinetic energy |
|---|---|---|---|
| Baseball pitch | 145 g | 95 mph | about 130 J |
| Runner | 150 lb | 6 mph | about 245 J |
| Cyclist and bike | 200 lb | 15 mph | about 2 kJ |
| Car | 3,300 lb | 65 mph | about 630 kJ |
Why it matters on the road
The energy a car must shed to stop grows with the square of speed, and so does the braking distance. A car that stops in 45 feet from 30 mph needs about 180 feet from 60 mph, on top of the distance covered during your reaction time. In a collision, the same energy is spent deforming the vehicles and the people inside; seat belts and crumple zones work by spreading it over a longer time.