A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a$($t$)=66$ta$($t$)=66$t$,$ at which time the fuel is exhausted and it becomes a freely "falling" body. $1515$ seconds later, the rocket's parachute opens, and the $($downward$)$ velocity slows linearly to $23$ft$/$s$-23$ft$/$s in $5$s$5$s$.$ The rocket then "floats" to the ground at that rate.