  Observations of early-type dwarf galaxies in clusters often show that cluster
dwarf members have significantly higher velocities and less symmetric
distributions than cluster giant ellipticals, suggesting that these dwarfs are
recently accreted galaxies, possibly from an infalling group. We use a series
of $N$-body simulations, exploring a parameter space of groups falling into
clusters, to study the observed velocity distributions of the infall components
along various lines of sight. We show that, as viewed along a line of sight
parallel to the group's infall direction, there is a significant peculiar
velocity boost during the pericentric passage of the group, and an increase in
velocity dispersion that persists for many Gyr after the merger. The remnants
of the infalling group, however, do not form a spatially distinct system --
consistent with recent observations of dwarf galaxies in the Virgo and Fornax
clusters. This velocity signature is completely absent when viewed along a
direction perpendicular to the merger. Additionally, the phase-space
distribution of radial velocity along the infall direction versus
cluster-centric radius reveals the separate dynamical evolution of the group's
central core and outer halo, including the presence of infalling remnants
outside the escape velocity envelope of the system. The distinct signature in
velocity space of an infalling group's galaxies can therefore prove important
in understanding the dynamical history of clusters and their dwarfs. Our
results suggest that dwarf galaxies, being insensitive to dynamical friction,
are excellent probes of their host clusters' dynamical histories.
