quantum mechanics deals with each and every particle of a system.in this case we are dealing with a single particle only i.e electron.hence we use quantum mechanics for it. however we use newtonian mechanics for a system having a collection of particles and we consider only the collective behavior of the system and not the behavior of each and every particle.a moving car(in this case) is a collection of particles(metal particles+paint particles etc etc).thus newtonian mechanics is applicable in this case!!