mathematics-physics-wiki/docs/en/physics/classical-mechanics/newtonian-mechanics/momentum.md

Momentum

Definition 1: the momentum \mathbf{p} of a particle is defined as the product of the mass and velocity of the particle

\mathbf{p} = m \mathbf{v},

with m the mass of the particle and \mathbf{v} the velocity of the particle.

For the case that \mathbf{v}: t \to \mathbf{v}(t) \implies \mathbf{v}'(t) = \mathbf{a}(t) we have the following theorem.

Theorem 1: let \mathbf{v}, \mathbf{a} be the velocity and acceleration of a particle respectively, if we have

\mathbf{v}: t \to \mathbf{v}(t) \implies \forall t \in \mathbb{R}: \mathbf{v}'(t) = \mathbf{a}(t),

then

\mathbf{p}'(t) = \mathbf{F}(t),

for all t \in \mathbb{R}.

??? note "Proof:"

Will be added later.