A launch assist force is modeled by $F\left(t\right)=20t^2$ N. What is the impulse during the $1.5$ s interval beginning $2.0$ s after ignition?

$285\text{ N}\cdot \text{s}$

$857.5\text{ N}\cdot \text{s}$

$232.5\text{ N}\cdot \text{s}$

$116.25\text{ N}\cdot \text{s}$