We are given a graph of position vs time. We are asked to determine the speed at 5 seconds. To do that we need to determine the slope of the line above the time point of 5 seconds. To determine the slope of the line we will use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
This means that we need to choose two points in the line. We use the graph to determine these points as follows:
The points we have chosen are:
[tex]\begin{gathered} (x_1,y_1)=(0,0)_{} \\ (x_2,y_2)=(10,5) \end{gathered}[/tex]
Replacing in the formula for the slope we get:
[tex]m=\frac{5-0}{10-0}[/tex]
Solving the operations:
[tex]m=\frac{5}{10}=\frac{1}{2}[/tex]
Therefore, the speed at 5 seconds is 0.5 meters per second.
For part B the following points can be taken:
