Answer
$p = (30.0~N\cdot s)~\hat{i}$
Work Step by Step
To find the impulse on the car, we can calculate the area under the force versus time graph.
From $t = 0$ to $t = 4.0~s$, the area can be divided into two parts, including a triangle (0 to 2 s) and a rectangle (2 s to 4 s)
We can find each area separately:
$A_1 = \frac{1}{2}(10.0~N)(2.0~s) = 10.0~N\cdot s$
$A_2 = (10.0~N)(2.0~s) = 20.0~N\cdot s$
We can find the impulse from $t = 0$ to $t = 4.0~s$:
$J = 10.0~N\cdot s +20.0~N\cdot s = 30.0~N\cdot s$
The change in the car's momentum will be equal to the impulse. Since the car started at rest, $p = 30.0~N\cdot s$
We an express the momentum in unit-vector notation:
$p = (30.0~N\cdot s)~\hat{i}$
