Why must acceleration be constant for the following equation to work?

Question

avg. velocity = (initial velocity + final velocity) / 2

Answer 1

Think of a graph of speed as a function of time. A constant acceleration gives a straight line (at a constant gradient). The above equation adds the y values of the two end points of the line and divides by two, giving the y value in the centre of the line. If the line was curved this would not work.

Answer 2

To derive this by integrating a=dv/dt from t_ini to t_fin, you must assume a is constant.

Answer 3

because it's a LINEAR relationship / equation

if acceleration changes then it's 2nd order
and Newtons laws of motion then apply
(with squared terms)