At time t

$=0$ a $2310$ 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$2$

$,$ where t

is time, and has a magnitude of $781\mathrm{.}25$ N

when t

$=1\mathrm{.}43$ s

$.$

Find the SI value of the constant A

$.$

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?

Express your answer with the appropriate units.