Scientific Ontology

v

Mechanics

Velocity

Rate of change of position.

metre per second (m/s)

Dimension: $[\,L T^{-1}\,]$

How values of velocity span the physical world (in m/s, log scale).

Continental drift

10^-9 m/s

Walking

1.40 × 10⁰ m/s

Sound (air)

3.43 × 10² m/s

Speed of light

3.00 × 10⁸ m/s

Lower limit10^-9 m/sUpper limit3.00 × 10⁸ m/s

Linear Momentum

\vec{p} = m\vec{v}

Kinetic Energy

E_k = \tfrac{1}{2} m v^2

Lorentz Force

\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})

Lorentz Factor

\gamma = \dfrac{1}{\sqrt{1 - v^2/c^2}}

SUVAT (velocity)

v = u + at

SUVAT (displacement)

s = ut + \tfrac{1}{2}at^2

SUVAT (velocity squared)

v^2 = u^2 + 2as

Centripetal Acceleration

a = \dfrac{v^2}{r} = r\omega^2

Centripetal Force

F = \dfrac{mv^2}{r} = mr\omega^2

Hubble's Law

v = H_0 d

Circular Motion (speed)

v = \omega r

Stokes' Law

F = 6\pi\eta rv

Magnetic Force on a Moving Charge

F = Bqv\sin\theta

Drift Velocity

I = nqvA

Redshift

z = \dfrac{\Delta\lambda}{\lambda} \approx \dfrac{v}{c}