I know what it means to say that my position is "X" at a particular moment in time. I can easily take a picture of my motion and observe my exact location at the instant the picture was taken. That is to say, my instantaneous position can be measured.
However, could I ever measure my velocity at an exact point in time? At best, it seems I can only estimate it based on the approximate derivative of my position or approximate integral of my acceleration over some measure of time.
Each of these methods, however, requires some elapse of time to perform the calculation, and even then it's only approximate. Neither allows me to know what my precise velocity is at an exact point in time, i.e. my instantaneous velocity is not being reported.
We obviously have devices like speedometers, tachometers, heat sensors, and dynos which ostensibly report quantities like velocity, heat flux, and power in real time. But really, how could they? Each of these quantities is itself the time derivative of another quantity and thus requires the passage of time to estimate (although velocity may be a bad example because we have things like pitot-static tubes).
Am I correct in surmising that rate-based instruments are not reporting in real-time? And if this is true, could we ever construct a device which did measure derivative quantities directly? What exactly would it measure?