2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217334The Newton equation describing the particle motion in constant external field force on canonical, Lie-algebraic and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent, while in the case of Lie-algebraic noncommutativity, when spatial coordinates commute to the time variable, the additional acceleration of particle is generated. We also indicate, that in the case of spatial coordinates commuting in Lie-algebraic way, as well as for quadratic deformation, there appear additional velocity and position-dependent forces.14 pages, 2 figures, v2: three references added, v3: accepted for publication in Physical Review D, v4: the page numbers for all references in preprint version are providedMathematical PhysicsHigh Energy Physics - Theorytext