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Newton's Second Law of Motion

Force equals mass times acceleration: \vec{F} = m\vec{a}, relating force, mass, and acceleration in a linear manner.
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The statement of the theorem

Consider a system SS of particles with mass mm and position vector r⃗(t)\vec{r}(t) in an inertial reference frame I\mathcal{I}. The law is fundamentally stated as the rate of change of linear momentum p⃗\vec{p} being equal to the net external force F⃗net\vec{F}_{net}. Mathematically, this is expressed as:\n\nF⃗net=dp⃗dt=ddt(mv⃗)\vec{F}_{net} = \frac{d\vec{p}}{dt} = \frac{d}{dt}(m\vec{v})\n\nFor a system described by a continuous body occupying a volume V(t)V(t), the governing equation is derived from the Cauchy momentum equation, which relates the divergence of the stress tensor σij\sigma_{ij} to the external body force density f⃗\vec{f}: \n\n∂∂xjσij+fi=ρd2xidt2\frac{\partial}{\partial x_j} \sigma_{ij} + f_i = \rho \frac{d^2 x_i}{dt^2} \n\nWhere ρ\rho is the mass density, σij\sigma_{ij} is the Cauchy stress tensor, and fif_i represents the external body forces (e.g., gravity). In the simplified case of a single particle with constant mass mm and no external body forces, this reduces to the classical form:\n\nF⃗net=ma⃗=md2r⃗dt2\vec{F}_{net} = m\vec{a} = m \frac{d^2 \vec{r}}{dt^2}
Source: Wikipedia