We describe pulse propagation through a slab with periodic dielectric function εc(t), thus extending our previous investigation for monochromatic incidence [Phys. Rev. A 79, 053821 (2009)]. Based on the concepts of phase and group delays, we prove that, for an incident quasi-monochromatic pulse, the transmitted pulse can be expressed as a superposition of partial pulses that are exact replicas of the incident pulse and that exit the slab with a time delay. These partial pulses have harmonic carrier frequencies ωc −nΩ (n is an integer, ωc is the carrier frequency of the incident pulse, and Ω = 2π/T is the slab modulation frequency). We find numerically that these partial pulses can be fast (peak velocity vn > c or vn < 0) or slow (vn ≪ c). Further, we investigate the peak velocity vp of the outcoming pulse for several cases. We find that this peak velocity vp and the partial peak velocities vn do not diverge —as occurs to the group velocity vg of the bulk dynamic-periodic medium when ωc = Ω/2. We expect that these results could be verified in the microwave regime [see Halevi et al., Proc. SPIE 8095, 80950I (2011)].