Answer
The change in momentum of the puck is $~~16.0~kg~m/s$
Work Step by Step
We can find $t$ when $F = 0$:
$12.0-3.00~t^2 = 0$
$t^2 = 4.00$
$t = 2.00~s$
We can find the impulse between $t = 0$ and $t = 2.00~s$:
$J = \int^{2.00}_{0}(12.0-3.00~t^2)~dt$
$J = (12.0~t-t^3)\Big\vert^{2.00}_{0}$
$J = [(12.0)(2.00)-(2.00)^3)]- [(12.0)(0)-(0)^3)]$
$J = (24.0-8.00)-(0)$
$J = 16.0~kg~m/s$
The change in momentum of the puck is equal to the impulse on the puck from the force.
The change in momentum of the puck is $~~16.0~kg~m/s$
