We are given a graph of position vs time. We are asked to determine the following.
Part 1. To determine the displacement we will use the following formula:
[tex]d=p_f-p_0[/tex]Where:
[tex]\begin{gathered} p_f,p_0=\text{ final and initial position} \\ d=\text{ displacement} \end{gathered}[/tex]The final position is the position at "t = 24s" and the initial position is at "t = 0s". From the graph we have:
[tex]\begin{gathered} p_f=0 \\ p_0=12m \end{gathered}[/tex]Now, we plug in the values:
[tex]d=0-12m=-12m[/tex]Therefore, the displacement is -12 meters.
Part 2. We are asked to determine the total distance from 0s to 24s. To do that we will determine the displacements from 0 to 8s, from 8s to 16s, and from 16s to 24s:
[tex]s=\lvert{d_{0-8}}\rvert+\lvert{d_{8-16}}\rvert+\lvert{d_{16-24}}\rvert[/tex]Now, we plug in the initial and final values:
[tex]s=\lvert{6m-12m}\rvert+\lvert{6m-6m}\rvert+\lvert{0-6m}\rvert[/tex]Solving the operations we get:
[tex]s=\lvert{-6m}\rvert+\lvert{0m}\rvert+\lvert{-6m}\rvert=6m+6m=12m[/tex]Therefore, the total distance is 12 meters.