A time$-$varying horizontal force $F(t)=A{t}^4+B{t}^2$ acts for $0\mathrm{.}500$ s on a $12\mathrm{.}25-kg$ object, starting at time $t=1\mathrm{.}00s.$ In the SI system, A has the numerical value $4\mathrm{.}50$ and $B$ has the numerical value $8\mathrm{.}75.$

$($a$)$ What are the SI units of A and $B?$

$($b$)$What magnitude of impulse does this force impart to the object?