At time $1=0$ a $2150$ kg rocket in outer space fires an engine that exerts an increasing force on it in the $+$x$-$direction. This force obeysthe equation F$,=$ A$?,$ where t is time, and has a magnitude of $781\mathrm{.}25$ Nwhen $1=1\mathrm{.}25$ 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 $1\mathrm{.}50$ s interval starting $2\mathrm{.}00$ s after the engine is fired? $($c$)$ By how much does the rocket's velocity change during this interval? Assume constant mass.