To find the change in momentum, we need to calculate the impulse, which is the area under the force-time graph.$\\$The graph consists of three distinct regions:$\\$• A triangle from $t = 0$ to $t = 2$ s$\\$• A rectangle from $t = 2$ to $t = 4$ s$\\$• A rectangle from $t = 4$ to $t = 8$ s$\\$1. Calculate the area of the triangle ($t = 0$ to $t = 2$ s):$\\$Base $= 2$ s, Height $= 6$ N$\\$Area of triangle $= \frac{1}{2} \times$base$\times$height$\\ = \frac{1}{2} \times 2 \times 6 = 6$ Ns$\\$2. Calculate the area of the rectangle ($t = 2$ to $t = 4$ s):$\\$Width $= 2$ s, Height $= 3$ N$\\$Area of rectangle $=$width$\times$height$\\ = 2 \times 3 = 6$ Ns$\\$3. Calculate the area of the rectangle ($t = 4$ to $t = 8$ s):$\\$Width $= 4$ s, Height $= -3$ N$\\$Area of rectangle $=$width$\times$height$\\ = 4 \times (-3) = -12$ Ns$\\$Total impulse (change in momentum) is the sum of these areas:$\\ \Delta p = 6 + 6 - 12 = 0$ Ns$\\$The change in momentum of the particle over the time interval from zero to 8 s is $0$ Ns.$\\$This corresponds to Option 3.