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We discuss the definition of velocity as dE/dp, where E,p are the energy andmomentum of a particle, in Doubly Special Relativity (DSR). If this definitionmatches dx/dt appropriate for the space-time sector, then space-time can inprinciple be built consistently with the existence of an invariant lengthscale. We show that, within different possible velocity definitions, aspace-time compatible with momentum-space DSR principles can not be derived.Comment: 11 pages, no figures, minor changes, references added, final version  to appear in PR

Approaching space-time through velocity in doubly special relativity