A plane making a loop with a radius of p $=1\mathrm{.}00$ mi is being tracked by a radar at O$.$ The plane has coordinates $($x$,$ y$)=(3,100,1,900)$ feet measured from O$,$ and is traveling at a horizontal velocity of $350$ mph$,$ while accelerating horizontally at a rate of $12$ ft$/$s$2.$

Determine the second rate of change

about the radar dish in rad$/$s$2$