  We investigate the kinetics of a nonrelativistic particle interacting with a
constant external force on a Lie-algebraic noncommutative space. The structure
constants of a Lie algebra, also called noncommutative parameters, are
constrained in general due to some algebraic properties, such as the
antisymmetry and Jacobi identity. Through solving the constraint equations the
structure constants satisfy, we obtain two new sorts of algebraic structures,
each of which corresponds to one type of noncommutative spaces. Based on such
types of noncommutative spaces as the starting point, we analyze the classical
motion of the particle interacting with a constant external force by means of
the Hamiltonian formalism on a Poisson manifold. Our results {\em not only}
include that of a recent work as our special cases, {\em but also} provide new
trajectories of motion governed mainly by marvelous extra forces. The extra
forces with the unimaginable $t\dot{x}$-, $\dot{(xx)}$-, and
$\ddot{(xx)}$-dependence besides with the usual $t$-, $x$-, and
$\dot{x}$-dependence, originating from a variety of noncommutativity between
different spatial coordinates and between spatial coordinates and momenta as
well, deform greatly the particle's ordinary trajectories we are quite familiar
with on the Euclidean (commutative) space.
