  We consider the space-like D$p$ brane solutions of type II string theories
having isometries ISO$(p+1)$ $\times$ SO$(8-p,1)$. These are asymptotically
flat solutions or in other words, the metrics become flat at the time scale
$\tau \gg \tau_0$. On the other hand, when $\tau \sim \tau_0$, we get $(p+1)+1$
dimensional flat FLRWmetrics upon compactification on a $(8-p)$ dimensional
hyperbolic space with time dependent radii. We show that the resultant
$(p+1)+1$ dimensional metrics describe transient accelerating cosmologies for
all $p$ from 1 to 6, i.e., from $(2+1)$ to $(7+1)$ space-time dimensions. We
show how the acceleration changes with the interplay of the various parameters
characterizing the solutions in $(3+1)$ dimensions. Finally, for $\tau \ll
\tau_0$, after compactification on $(8-p)$ dimensional hyperbolic space, the
resultant metrics are shown to take the form of $(p+1)+1$ dimensional de Sitter
spaces upto a conformal transformation. Cosmologies here are decelerating, but,
only in a particular conformal frame we get eternal acceleration.
