Answer
The graph of the corresponding velocity function is given below.
Work Step by Step
Firstly the divide the time into three intervals $[0,6]$, $[6,8]$ and $[8,10]$.
Now, since in all three intervals, the distance and the time are linearly dependent.
The slope will be a different constant number for all three intervals.
Since the slope of the graph of distance and time is equal to velocity.
There will be three different constant velocities in all three intervals.
To calculate the slope or the constant velocity in the interval $[0,6]$. Use the formula of the slope.
That is, slope $=\dfrac{y_2-y_1}{x_2-x_1}$
Use the points $(0,0)$ and $(6,5)$.
We get, slope $=\dfrac{5-0}{6-0}=\dfrac{5}{6}$
So, velocity $v=\dfrac{5}{6}$ in the interval $[0,6]$.
To calculate the slope or the constant velocity in the interval $[6,8]$. Again use the formula of the slope.
That is, slope $=\dfrac{y_2-y_1}{x_2-x_1}$
Use the points $(6,5)$ and $(8,5)$.
We get, slope $=\dfrac{5-5}{8-6}=0$
So, velocity $v=0$ in the interval $[6,8]$.
To calculate the slope or the constant velocity in the interval $[8,10]$. Use the formula of the slope.
That is, slope $=\dfrac{y_2-y_1}{x_2-x_1}$
Use the points $(8,5)$ and $(10,6)$.
We get, slope $=\dfrac{6-5}{10-8}=\dfrac{1}{2}$
So, velocity $v=\dfrac{1}{2}$ in the interval $[8,10]$.
Now plot the velocity functions in the three intervals as follows.
