We are given a graph of distance (x) versus time (t). We are asked to determine the displacement between the following points:
[tex]\begin{gathered} t_1=2.0s \\ t_2=4.0s \end{gathered}[/tex]
To do that, we need to have into account that the displacement is given by:
[tex]\Delta x=x_2-x_1[/tex]
Where:
[tex]\begin{gathered} \Delta x=\text{ displacement} \\ x_2=\text{ x position at t2} \\ x_1=\text{ x position at t1} \end{gathered}[/tex]
We determine first the value of "x" when t = 2.0 seconds, which will be x1. We use the graph to determine the value of "x" as follows:
We notice that at t = 2.0s, the value of "x" is 0, therefore:
[tex]x_1=0[/tex]
Now, we do the same for the value of t = 4.0s, we get:
We notice that the value of "x" is also 0 at t = 4.0s, therefore:
[tex]x_2=0[/tex]
Now, we substitute in the formula for the displacement:
[tex]\begin{gathered} \Delta x=0-0 \\ \Delta x=0 \end{gathered}[/tex]
Therefore, the displacement between t = 2.0 and t = 4.0 is 0.
The same procedure can be used for the other time frames. Not necessarily all the displacements are 0 or the values of "x" are 0.
