Systems of differential equations describing acceleration of a car in both cases: with and without slipping of driving wheels are derived. Front-drive and rear-drive cars are considered. The conditions of arising and termination of slipping are discussed. The moment of rolling friction acting on the driving wheels, and their moments of inertia are taken into consideration to obtain the refined dynamical condition of realization of the constraint. In this case we consider a reduced moment of inertia, which includes rotating masses of cardan shaft, details of transmission gear-box, flywheel, crankshaft, etc. connected to the driving wheels, as the moment of inertia of driving wheels. It is noted that this quantity depends, in general, on the relation between angular velocities of driving wheels and engine. The jumps of car acceleration and driving force, which are an interesting peculiarity of car acceleration with slipping of driving wheels, are theoretically found. Computational results are presented. The calculations obtained by the refined and the simplified dynamical conditions of realization of the constraint imposed on the driving wheels are compared. It is shown that in the latter case the jumps of car acceleration and driving force are observed not only when slipping terminates but also when it starts.