Answer
The graph of the corresponding position function is shown below.
Work Step by Step
Firstly divide the time into three intervals $[0,6]$, $[6,8]$ and $[8,10]$.
In the interval $[0,6]$, velocity is constant and equal to $40$.
Since velocity is constant, the position function will be a linear function with slope $=40$.
At the time $t=0$, the position will also be zero.
Thus $(0,0)$ will lie on the graph of the position function.
Now use slope-intercept form of the equation of the line.
We get, position function $d-0=40(t-0)$ or $d=40t$.
Now calculate $d$ at time $t=6$.
We get, $d=40\times6=240$
Thus, $(6,240)$ is a point on the graph of the position function of the interval $[6,8]$.
Since, the velocity is zero in the interval $[6,8]$, the slope of the graph of position function will also be zero.
Now again use slope-intercept form of the equation of the position function.
We get, $d-240=0(t-6)$ or $d=240$
Since the position is constant in the interval $[6,8]$.
We get, $d=240$ at $t=8$.
Thus, $(8,240)$ is a point on the graph of the position function of the interval $[8,10]$.
Since, the velocity is constant and equals to $60$ in the interval $[8,10]$, the slope of the graph of position function will also be $60$.
Again, use slope-intercept form of an equation of the position function.
We get, $d-240=60(t-8)$ or $d=60t-480+240=60t-240$
Now plot the three equations of the position function as follows.
