In the context of multiple view geometry in any dimension, we compute the minimum number of views necessary for projective reconstruction of both the set of cameras and of scenes. Within a unified approach to critical configurations and their loci, the paper focuses on the case of dynamic scenes of multiple bodies traveling along parallel straight-line trajectories with constant velocities, in the framework of higher dimensional projections introduced by Shashua and Wolf. Critical loci in this case are explicitly determined. A stratification of the resulting locus in terms of fixed common velocities is presented and leveraged to show, via a number of simulated experiments, instability of the reconstruction near critical configurations.