Instantaneous Velocity
Instantaneous velocity is an object's velocity at a single moment rather than over an interval. AP Physics 1 defines it as the rate of change of position, read off a position versus time graph as the slope of the tangent at that point.
That is EK 1.3.A.4.i, word for word in its own terms: an object's instantaneous velocity is the rate of change of the object's position, which is equal to the slope of a line tangent to a point on a graph of the object's position as a function of time.
How an algebra-based course gets there without derivatives. EK 1.2.B.5 supplies the bridge. Calculating average velocity over a very small time interval yields a value very close to the instantaneous velocity. Shrink the interval and the secant line rotates into the tangent. AP Physics C: Mechanics writes the same idea as in EK 1.2.C.1.i, but AP Physics 1 never needs the notation.
It is also what decides whether your lab data is the right number. The CED's photogate section says the speed a photogate measures may be the object's instantaneous speed at that single location, or the average speed between two different photogates, depending on how the gates are configured, and that in some applications the distinction is crucial to obtaining the appropriate value. One gate and a narrow card gives an interval that is small but not zero, so the reading approximates the instantaneous value rather than equaling it.
Say [velocity](/glossary/velocity) with no qualifier and you mean this one. Average velocity is the one that needs its adjective. On a position graph, a steeper tangent is faster and a negative slope is motion in the negative direction; where the tangent is flat the object is momentarily at rest, which is not the same as having zero acceleration. The side-by-side treatment is in average vs instantaneous velocity.