I don't know what you mean by "a single instance" in this case. If you mean "instant", then that would be an infinitesemal unit of time during which you could cover in an infinitesemal distance in space (ds/dt). What you suggest is that if you plot position over time, you can't ever identify the slope of the tangent line at a given point, but of course you can do that with calculus using limits. There is no rate of change between a point and itself, but the instantaneous velocity at that point does represent an actual physical quantity, kinetic energy, with respect to the object's mass.
In a physical sense, you can't really look at "zero" time because of the continuous "analog" nature of the universe. You can look at smaller and smaller units of time, but you actually can't get to zero. On a subatomic scale, you end up hitting a fundamental limit of being able to know both position and momentum (mass*velocity) of a particle simultaneously. That's the kind of weirdness that gives you cats that are both dead and alive.