  In the framework of the augmented superfield formalism, the local, covariant,
continuous and off-shell (as well as on-shell) nilpotent (anti-)BRST symmetry
transformations are derived for a $(0 + 1)$-dimensional free scalar
relativistic particle that provides a prototype physical example for the more
general reparametrization invariant string- and gravitational theories. The
trajectory (i.e. the world-line) of the free particle, parametrized by a
monotonically increasing evolution parameter $\tau$, is embedded in a
$D$-dimensional flat Minkowski target manifold. This one-dimensional system is
considered on a $(1 + 2)$-dimensional supermanifold parametrized by an even
element $\tau$ and a couple of odd elements ($\theta$ and $\bar\theta$) of a
Grassmannian algebra. The horizontality condition and the invariance of the
conserved (super)charges on the (super)manifolds play very crucial roles in the
above derivations of the nilpotent symmetries. The geometrical interpretations
for the nilpotent (anti-)BRST charges are provided in the framework of
augmented superfield approach.
