Momentum derivative of kinetic energy is speed¶

The general formula for the kinetic energy of an object features its speed and momentum. This way it can be used not only in the case of variable mass, but also in the relativistic case.

Links:

Wikipedia, derivable from here.

speed¶: The speed of the object.

Symbol:: v
Latex:: \(v\)
Dimension:: velocity

momentum¶: The momentum of the object as a function of speed.

Symbol:: p(v)
Latex:: \(p{\left(v \right)}\)
Dimension:: momentum

kinetic_energy¶: The kinetic_energy of the object as a function of momentum.

Symbol:: K(p(v))
Latex:: \(K{\left(p{\left(v \right)} \right)}\)
Dimension:: energy

law¶

Derivative(K(p(v)), p(v)) = v

Latex:: \[\frac{d}{d p{\left(v \right)}} K{\left(p{\left(v \right)} \right)} = v\]