Quantifying the outcomes of cells collisions is a crucial step in building
the foundations of a kinetic theory of living matter. Here, we develop a
mechanical theory of such collisions by first representing individual cells as
extended objects with internal activity and then reducing this description to a
model of size-less active particles characterized by their position and
polarity. We show that, in the presence of an applied force, a cell can either
be dragged along or self-propel against the force, depending on the polarity of
the cell. The co-existence of these regimes offers a self-consistent mechanical
explanation for cell re-polarization upon contact. We rationalize the
experimentally observed collision scenarios within the extended and particle
models and link the various outcomes with measurable biological parameters