$7.(15$ pts$)$ At time t $=0,$ a $2150-$kg rocket in outer space fires an engine that exerts an increasing force on it in the x$-$direction. This force obeys the equation Fx $=$ At$2$ B$,$ where t is time and B $=215$ N$.$ The force Fx has a magnitude of $781\mathrm{.}25$ N when t $=1\mathrm{.}25$ s$.($a$)$ Find the SI value of the constant A$,$ including its units. $($b$)$ What impulse does the engine exert on the rocket during the $1\mathrm{.}25-$s interval starting $2\mathrm{.}50$ s after the engine is fired? $($c$)$ By how much does the rocket$$s velocity change during this interval?