  A new expression to the total age of the Universe is derived in terms of the
average deceleration parameter. This kinematic result holds regardless of the
curvature of the universe as well as of the underlying gravity theory. It
remains valid even in the context of brane-world motivated cosmologies. Since
the present age parameter of the Universe is accurately adjusted to $H_0t_0 =
1$, it is shown that the time averaged value of the deceleration parameter is
zero. This also means that the cosmic age today is exactly the one predicted by
a relativistic flat cosmological model filled by K-matter, a fluid satisfying
the equation of state $p = -{{1/3}}\rho$. By assuming the validity of this
relation (in an average long time meaning), it is argued that the decelerating
stages of the expansion must exactly be compensated by the accelerated phases,
as if the observed Universe coasts forever. If this is true, the present
accelerating stage must be followed by a subsequent decelerating phase as
predicted by some recent scalar field and brane-world motivated cosmologies.
