Instantaneous speed

A speed that changes at every instant

When you look at a car's speedometer, the needle keeps moving: it shows the instantaneous speed, that is, the speed of the vehicle at a precise instant, not over the whole trip.

Difference from average speed

Average speed is calculated over an entire duration (v = d/t over the whole trip). Instantaneous speed, on the other hand, corresponds to a very short instant, almost "immediate".

Average speed	Instantaneous speed
Over the whole trip	At a given instant
A single value for the trip	Changes at every instant
v = total distance / total time	Read on a speedometer or calculated over a very small interval

How is it estimated?

In practice, instantaneous speed is approximated by measuring a very small distance covered over a very small time interval, around the instant of interest.

Example: an automatic speed camera measures the position of a car at two very close instants (a few milliseconds apart) to estimate its instantaneous speed at the moment of the check.

Classic pitfall

Never say that a vehicle "travels at a constant average speed" throughout a trip with traffic lights, bends, and hills: it is its instantaneous speed that keeps varying, even though its average speed remains a single overall value calculated afterward, once the trip is over.