Astrophysical sources of relativistic jets or outflows, such as gamma-ray bursts (GRBs), active galactic nuclei (AGN) or micro-quasars, often show strong time variability. Despite such impulsive behaviour, most models of these sources assume a steady state for simplicity. Here I consider a time-dependent outflow that is initially highly magnetized and divided into many well-separated sub-shells, as it experiences impulsive magnetic acceleration and interacts with the external medium. In AGN the deceleration by the external medium is usually unimportant and most of the initial magnetic energy is naturally converted into kinetic energy, leading to efficient dissipation in internal shocks as the sub-shells collide. Such efficient low-magnetization internal shocks can also naturally occur in GRBs, where the deceleration by the external medium can be important. A strong low-magnetization reverse shock can develop, and the initial division into sub-shells allows it to be relativistic and its emission to peak on the time-scale of the prompt GRB duration (which is not possible for a single shell). Sub-shells also enable the outflow to reach much higher Lorentz factors that help satisfy existing constraints on GRBs from intrinsic pair opacity and from the afterglow onset time.