Question

How do you find the displacement step by step between t=2.0s to t=4.0s, t=0s to t=4s, and t=1.0s to t=3.0s?

Answer 1

We are given a graph of distance (x) versus time (t). We are asked to determine the displacement between the following points:

`\begin{gathered} t_1=2.0s \\ t_2=4.0s \end{gathered}`

To do that, we need to have into account that the displacement is given by:

`\Delta x=x_2-x_1`

Where:

`\begin{gathered} \Delta x=\text{ displacement} \\ x_2=\text{ x position at t2} \\ x_1=\text{ x position at t1} \end{gathered}`

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:

`x_1=0`

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:

`x_2=0`

Now, we substitute in the formula for the displacement:

`\begin{gathered} \Delta x=0-0 \\ \Delta x=0 \end{gathered}`

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.