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How to calculate average velocity

The position of an object moving along X-axis is given as $X=a+bt^2$ where $a=8.5\,\mathrm m$, $b=2.5\,\mathrm {m/s^2}$ and $t$ is measured in seconds. What is it's velocity at $t=0$ and $t=2.0$ s? ...
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Average velocity = Arithmetic Mean

I am having trouble grasping how the average velocity of a particle between an initial position and final position equals to the arithmetic mean of the initial velocity and the final velocity when the ...