both cases are covered by classical physics. corrections from relativistic are completely neglected if You take maximal speed of a car. the most hard part is how to take just one direction velocity by human jump from the car.
-
So why we use classical field theory ? Or maybe by classical You mean (not correctly) just Newtonian physics ?
lol i was just trying to read a larger audience.. and in most intro texts (UG level) they refer to it as "relativistic physics" .. but yes the classical field theory differs from the QFT by the imposition of the canonical commutation relation on the degrees of freedom