A particle moves along the x axis. Its position is given by the equation x $=1\mathrm{.}6+2\mathrm{.}7$t $3\mathrm{.}9$t$2$with x in meters and t in seconds.$($a$)$ Determine its position when it changes direction. m$($b$)$ Determine its velocity when it returns to the position it had at t $=0?($Indicate the direction of the velocity with the sign of your answer.$)$ m$/$s