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| 1 | Three-dimensional acceleration in general relativity can be defined so that spinless particle in the process of evolution in an external gravitational field can not exceed the speed of light. We ask what happens if a spinless particle is replaced by test-particle with spin one-half. Inclusion of spin-gravitational interaction gives generalized Papapetrou equations with modified metric along the world-line. The modified metric should be used to calculate the acceleration of spinning particles. Inclusion of spin-electromagnetic interaction in flat space gives generalized Frenkel equations, where an effective metric along world-line arises for the particle with anomalous magnetic moment. This implies that intervals of time (and distance) probed by such particle in the presence of electromagnetic field slightly differ from those in empty space. Keywords: ultra-relativistic spinning particle, Frenkel equation, BMT equation, Papapetrou equation | 1572 | ||||