  In recent years, it was found that the energy $E_{c.m.}$ in the centre of
mass frame of two colliding particles can be unbounded near black holes. If
collision occurs exactly on the horizon, $E_{c.m.}$ is formally infinite.
However, in any physically reasonable situation this is impossible. We collect
different scenarios of such a kind and show why in every act of collision
$E_{c.m.}$ is indeed finite (although it can be as large as one likes). The
factors preventing infinite energy are diverse: the necessity of infinite
proper time, infinite tidal forces, potential barrier, etc. This prompts us to
formulate a general principle according to which the limits in which $E_{c.m.}$
becomes infinite are never achieved. We call this the kinematic censorship
(KC). Although by itself the validity of KC is quite natural, its application
allows one to forbid scenarios of collisions predicting infinite $E_{c.m.}$
without going into details. The KC is valid even in the test particle
approximation, so explanation of why $E_{c.m.}$ cannot be infinite, does not
require references (common in literature) to the non-linear regime,
backreaction, etc. The KC remains valid not only for free moving particles but
also if particles experience the action of a finite force. For an individual
particle, we consider a light-like continuous limit of a time-like trajectory
in which the effective mass turns into zero. We show that it cannot be
accelerated to an infinite energy during a finite proper time under the action
of such a force. As an example, we consider dynamics of a scalar particle
interacting with a background scalar field.
