Ultra-diffuse galaxies (UDGs) are spatially extended, low surface brightness stellar systems with regular elliptical-like morphology found in a wide range of environments. Studies of the internal dynamics and dark matter content of UDGs that would elucidate their formation and evolution have been hampered by their low surface brightnesses. We identified a sample of low-mass early-type post-starburst galaxies in the Coma cluster still populated with young stars, which will passively evolve into UDGs in the next 5-10 Gyr. We collected deep observations for a large sample of low-mass galaxies in the Coma cluster using MMT Binospec. Here, we present spatially resolved velocity profiles out to 1 half-light radius, stellar velocity dispersions, ages, and metallicities for dozens of old UDGs in the Coma cluster and the same quantities derived out to 2-3 half-light radii for young dwarf post-starburst galaxies, the future UDGs. We derived their dynamical masses and dark matter content using Jeans modelling. High dark matter fractions, low degrees of rotational support, moderately low metallicities place UDGs onto the extension of the dwarf elliptical galaxy locus in several galaxy scaling relations such as the Fundamental Plane, the baryonic Tully-Fisher and the mass-metallicity relation. We demonstrate that statistically at least a half of present-day `old' UDGs were formed by ram-pressure stripping of disky progenitors. We discuss whether the same evolutionary scenario is applicable to the entire UDG population.
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