Question

define average velocity when the velocity of a body changes at a non uniform rate and a uniform rate.

Answer 1

 Average velocity = When an object moves along a straight line in the same direction, its total path length is the magnitude of displacement. Hence its average speed is equal to the magnitude of average velocity

Answer 2

Average velocity wrt time is the  total net displacement vector divided by total time duration.   That depends on the final position of the body, initial position and the time duration...
 
    The definition is always the same irrespective of the way velocity changes...   However, the way of finding could be simpler in case of uniform change in velocity..
 
   1) velocity changes at a uniform rate a...

$\vec{v2} = \vec{v1} + \vec{a} t\\v_{avg} = \frac{\vec{v_2} +\vec{v_1}}{2}=\vec{v1}+\frac{1}{2}\vec{a} t=\frac{1}{t}\vec{s}$
                     = average of the initial velocity and final velocity.

   2) velocity changes  at non uniform rate....

$v_{avg}=\frac{s}{t}=\frac{1}{t} \int\limits^t_0 {v(t)} \, dt =\frac{1}{t} \int\limits^t_0 {(v_0+a(t)*t)} \, dt$

   If the velocity changes direction also, then vector quantities should be used instead of scalar quantities in the above formulas..