Can we measure rates in real time? 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?
 A: Years ago, the speedometer in a car moved the needle by spinning a magnet. The physical rotation of the driveshaft turned the cable inside the assembly. The spinning cable is attached to a magnet. The needle is mounted on a disk attached to a spring which provides rotational counter-force. The spinning magnet attempts to spin the disk, but the spring provides a force to stop the spinning. The faster the magnet spins, the more force is applied to the disk to spin it. See Wikipedia and the bottom of this page.
I believe this is a measurement of speed in real time since at any moment you can state your speed. 
Also, the turning of the speedometer cable would turn the dial for the number of miles driven (which is why you could decrease the number of miles on the vehicle if you drove it backwards). This is a measurement of distance (the derivative of speed) in real time.
A: There are many devices that can measure rate of a quantity without using approximate derivative and integral. I will give some example here:


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*Pitot tube
Pitot tube is a device used to measure velocity of a body with respect to flow. This device uses Bernoulli's equation. For computing the velocity using Pitot tube, the total pressure and static pressure must be known which these two quantity could be measeured instantaneously. Here you can find more detail on Pitot tube.   

*Orifice plate
Orifice plate is used to measure mass or volumetric flow rate. This device also used Bernoulli's equation. For measuring mass flow rate (or volumetric rate) the pressure of the point before plate and the point after the plate must be known. Measuring these two pressure are very simple (e.g. by measuring the height of liquid column). More details can be found in many books and webpages (e.g. here).

*Hot wire
This device is used for measuring the velocity of a fluid flow. It used the laws of thermodynamics specially the first law and principles of electric circuits. Here you can find more details on this device.
A: How about a radar gun? It works by measuring the Doppler shift of a radio signal incurred when it bounces off a moving object. The frequency shift of each photon encodes the instantaneous speed of the object when the photon scattered off of it. Difficult to get much more instantaneous than that (especially when you compare to a measurement of position, which would often be achieved by receiving and analysing some photons).
