Given,
The initial velocity of the cart, u=10 m/s
The final velocity of th cart, v=0 m/s
The impulse is calculated as the area under the curve of the plot of force versus time.
Let us assume that the plot is a rectangle.
From the graph,
The length of the recatangle, t=4.5-0.5=0.5 s
The breadth of the rectangle is approximately, b