If I am correct, velocity ( instantaneous speed) is the derivative of distance.
Nowadays cars are equipped with electronic calculators, but previously that wasn't the case.
Hence my question : by which mechanical means did old speedometers manage to give an instantaneous rate of change ( in distance) , as if they could " calculate" a derivative?
Another problem: suppose a car is moving at time t, in order to calculate the velocity at t, the quotitient [s(t+h) - s(t)] / h must be defined ( for velocity is the limit of this quotient). But, at time t, the number s(t+h) is not defined ( for it is the distance the car will have travelled in some very close future instant).
So, could one say that the velocity given at time t by a speedometer cannot be anything else but a " retrospective " velovity?