Newton's second law

EK 2.5.A.2 states it as the acceleration of a system's center of mass having a magnitude proportional to the magnitude of the net force on the system, in the same direction as that net force. Force in newtons, mass in kilograms, acceleration in m/s$^2$.

The AP Physics 1 equation sheet prints the system form, $\vec{a}_{sys} = \frac{\sum \vec{F}}{m_{sys}} = \frac{\vec{F}_{net}}{m_{sys}}$, and separately $\vec{F}_{net} = \frac{\Delta \vec{p}}{\Delta t} = m\frac{\Delta \vec{v}}{\Delta t} = m\vec{a}$. Both lines are the second law; the first is the one that names the system and its total mass.

It is a vector equation, which makes it one equation per axis. Resolve into components, then write $\sum F_x = ma_x$ and $\sum F_y = ma_y$ separately. Vertical equilibrium and horizontal acceleration coexist happily.

The force that goes in is the external net force: EK 2.5.A.3 restricts changes in the center-of-mass velocity to nonzero net external forces, so internal pushes never appear.

The procedure of choosing axes, summing forces and solving for $a$ belongs to how to find net force, with the net force calculator for the arithmetic. Topic 2.5 carries the AP framing.