  It was recently shown that velocity-dependent forces between parallel
fundamental strings moving apart in a $D-$dimensional spacetime implied an
accelerating expanding universe in $D-1$-dimensional space-time. Exact
solutions were obtained for the early time expansion in $D=5,6$. Here we show
that this result also holds for fundamental strings in the background of a
fivebrane, and argue that the feature of an accelerating universe would hold
for more general $p$-brane-seeded models.
