Derivation of the formula that the instantaneous velocity at the middle point of time is equal to the average velocity of the whole course Such as the title

Derivation of the formula that the instantaneous velocity at the middle point of time is equal to the average velocity of the whole course Such as the title

This is true for uniform motion and uniform acceleration
Uniform motion, obviously, at the same speed
Uniform acceleration: if the initial velocity is V0, the instantaneous velocity at the middle point is V0 + 1 / 2at,
S = v0t + 1 / 2at ^ 2, average velocity = s / T = V0 + 1 / 2at, so it is equal