The impulse that is delivered to the object is $vec{I} = 12.2 mathrm{~kg cdot m/s}$. The initial momentum of the object is $vec{p_{1}} = 4.5 mathrm{~kg cdot m/s}$.

$textbf{Required: }$

Finding the final momentum of the object.

According to the Momentum-Impulse Theorem:

$$
begin{align*}
vec{I} &= vec{F} ~ Delta t \
&= Delta vec{p} \
&= left( vec{p_{f}} – vec{p_{i}} right) \
end{align*}
$$

Rearrange and solve for the final momentum of the object:

$$
begin{align*}
vec{p_{f}} &= vec{I} + vec{p_{i}} \
&= 12.2 mathrm{~kg cdot m/s} + 4.5 mathrm{~kg cdot m/s} \
&= 16.7 mathrm{~kg cdot m/s} \
end{align*}
$$

So, the final momentum of the object is $16.7 mathrm{~kg cdot m/s}$.