Instantaneous acceleration

One instant, not one interval. Average acceleration divides a whole change in velocity by the whole time it took; instantaneous acceleration is the value at a single clock reading.

AP Physics 1 gets you there by shrinking the interval. EK 1.2.B.5 says that calculating average velocity or average acceleration over a very small time interval yields a value that is very close to the instantaneous velocity or instantaneous acceleration. EK 1.3.A.4.ii then makes it graphical: the instantaneous acceleration is the slope of a line tangent to a point on a graph of the object's velocity as a function of time.

AP Physics C: Mechanics finishes the sentence with calculus. EK 1.2.C.1.ii calls instantaneous acceleration the derivative of velocity with respect to time, printing $\vec{a} = d\vec{v}/dt$ and $a_x = dv_x/dt$.

Where it costs marks. Average and instantaneous acceleration coincide only when the acceleration is constant, which is the case the three kinematic equations describe. On a curved velocity-time graph they differ, and a Physics 1 boundary statement under topic 1.3 keeps that case qualitative: sketch it, do not compute it.

Zero velocity does not force zero instantaneous acceleration. A ball thrown straight up has $v = 0$ at the top, yet its velocity-time graph is a straight line of slope $-9.8$ m/s$^2$ that merely crosses the time axis there. The acceleration is 9.8 m/s$^2$ downward for the whole flight.