The graph shows the force which acts on an object over a time interval of 8.0 seconds - Scottish Highers Physics - Question 4 - 2016

To find the momentum gained, we calculate the area under the force vs. time graph, which gives us the impulse. The graph can be split into two parts: a rectangle and a triangle.

1. Rectangle (0 to 2 seconds): The width is 2 seconds, and height is 10 N, so the area is: $ext{Area}_{ ext{rectangle}} = ext{width} \times ext{height} = 2 \text{ s} \times 10 \text{ N} = 20 \text{ N s}$

2. Triangle (2 to 8 seconds): The base is 6 seconds (from 2 to 8 seconds), and the height is the difference from 10 N to 12 N, which is 2 N. Thus, the area is: $ext{Area}_{ ext{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \text{ s} \times 2 \text{ N} = 6 \text{ N s}$

Adding both areas together gives: $ext{Total Area} = 20 \text{ N s} + 6 \text{ N s} = 26 \text{ N s}$