  In this paper, we derive the non-commutative corrections to the maximal
acceleration in the Doplicher-Fredenhagen-Roberts (DFR) space-time and show
that the effect of the non-commutativity is to decrease the magnitude of the
value of the maximal acceleration in the commutative limit. We also obtain an
upper bound on the acceleration along the non-commutative coordinates using the
positivity condition on the magnitude of the maximal acceleration in the
commutative space-time. From the Newtonian limit of the geodesic equation and
Einstein's equation for linearised gravity, we derive the explicit form of
Newton's potential in DFR space-time. By expressing the non-commutative
correction term of the maximal acceleration in terms of Newton's potential and
applying the positivity condition, we obtain a lower bound on the radial
distance between two particles under the gravitational attraction in DFR
space-time. We also derive modified uncertainty relation and commutation
relation between coordinates and its conjugate, due to the existence of maximal
acceleration.
