A particle is initially at rest at the origin at t $=0\mathrm{.}00$ s$.$ From t $=0\mathrm{.}00$ s to t $=5\mathrm{.}00$ s its velocity changes according to v$($t$)=(3\mathrm{.}20$ m$/$s$2)$t$.$ From t $=5\mathrm{.}00$ s to t $=11\mathrm{.}00$ s its velocity changes according to v$($t$)=(16\mathrm{.}00$ m$/$s$)-(1\mathrm{.}50$ m$/$s$2)($t $-5\mathrm{.}00$ s$).$ From t $=11\mathrm{.}00$ s to t $=20\mathrm{.}00$ s its velocity does not change. What is the position of the particle at t $=19\mathrm{.}16?$