A motor vehicle having a safety device for protecting pedestrians or bicyclists that collide with the motor vehicle includes an airbag which, in the non-activated basic state, is arranged folded together on an automotive body and, in the activated deployed state, at least partially covers a frame around the windshield. In the activated state, the airbag stretches out a windshield cover in front of the windshield. The cover has a region in which a plurality of energy dissipators are distributed on the side of the cover facing the windshield. During an impact with a person's head, the region is pressed against the windshield. The energy dissipators cause prior damage to the windshield, such that the rigidity of the windshield in this region is reduced. The windshield thus yields upon impact of the head in the region.