  We present the time-dependent solutions corresponding to the dynamical
D-brane with angles in ten-dimensional type II supergravity theories. Our
solutions with angles are different from the known dynamical intersecting brane
solutions in supergravity theories. Because of our ansatz for fields, all warp
factors in the solutions can depend on time. Applying these solutions, we
construct cosmological models from those solutions by smearing some dimensions
and compactifying the internal space. We find the
Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological solutions with
power-law expansion. We also discuss the dynamics of branes based on these
solutions. When the spacetime is contracting in ten dimensions, each brane
approaches the others as the time evolves. However, for Dp-brane ($p\le 7$)
without smearing branes, a singularity appears before branes collide. In
contrast, the D6-D8 brane system or the smeared D(p-2)-Dp brane system with one
uncompactified extra dimension can provide an example of colliding branes (and
collision of the universes), if they have the same charges.
