If acceleration is constant and velocity starts at zero, the distance covered in a period of time is equal to the area under the plot of velocity versus time. That plot will be in the shape of a triangle, so the area will be

distance = (1/2)(t)(Vf).

The average velocity is the distance divided by the time it takes to cover that distance, so it is

Vave = distance/t = (1/2)(t)(Vf)/t = Vf/2

distance = (1/2)(t)(Vf).

The average velocity is the distance divided by the time it takes to cover that distance, so it is

Vave = distance/t = (1/2)(t)(Vf)/t = Vf/2