Kinetic Energy✓ verified
Physics / Mechanics · Translational kinetic energy
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| mass | m | kg | 1.0 | Mass of the body |
| velocity | v | m/s | 1.0 | Linear speed of the body |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| kinetic_energy | KE | J | Kinetic energy |
The science & history
Understanding the Parameters
- $m$ — more mass means more energy at the same speed (and more inertia to accelerate).
-
$v$ — energy scales as $v^{2}$: double the speed, quadruple the kinetic energy. Direction does not enter the scalar $KE$ (only the speed).
-
$KE$ — joules of energy associated with motion; convertible to heat, deformation, potential energy, etc., by work and collisions.
Derivation (Approaching a Proof)
Newton’s second law: $F = m a = m\,dv/dt$. Power delivered by the force is $P = F v = m v\,dv/dt$. Energy gained over a path is the integral of power:
$$KE = \int P\,dt = \int_0^{v} m v\,dv = \frac{1}{2} m v^{2},$$
starting from rest. Equivalently, work $W = \int F\,ds = \int m a\,ds = \int m v\,dv$ yields the same result (work–energy theorem). Rotational counterpart: Rotational Kinetic Energy.
History
The $mv^{2}$ form emerged in 17th–18th century vis viva debates (Leibniz, Huygens); the factor $\tfrac12$ and the modern kinetic-energy name solidified with 19th-century energy conservation (Thomson, Rankine, Helmholtz).
Related Concepts: Potential Energy, Work Constant Force, Momentum, Rotational Kinetic Energy, Power
Notes: Registry calculator kinetic-energy (unverified). Non-relativistic; for $v$ not near $c$.
Scalar speed form (not $\tfrac12 m\mathbf{v}\cdot\mathbf{v}$ written out).