Acceleration

Symbol $\vec{a}$, units m/s$^2$. Average acceleration is the change in velocity divided by the interval over which it changed, $\vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t}$, stated in AP Physics 1 EK 1.2.B.3. Instantaneous acceleration is the slope of the line tangent to a velocity-time graph, per EK 1.3.A.4.ii.

EK 1.2.B.4 sets the condition: an object is accelerating if the magnitude of its velocity is changing, or the direction is, or both. That is why uniform circular motion is accelerated motion even though the speedometer never moves.

Zero velocity does not mean zero acceleration. A ball thrown straight up has $v = 0$ at the top of its flight, but gravity has not switched off, so its acceleration there is still 9.8 m/s$^2$ downward. Acceleration describes how the velocity is changing, not how big it is.

A negative acceleration does not mean slowing down. Compare signs instead: when $a$ and $v$ carry the same sign the object speeds up, and when they carry opposite signs it slows down. A ball falling with $v = -3$ m/s and $a = -9.8$ m/s$^2$ is speeding up.

The constant-acceleration algebra belongs to the kinematic equations guide. For the cause rather than the description, see net force.