Acceleration varies as a = A t(T−t) during 0≤t≤T. The average acceleration in this interval is:

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G1 Physics · Accepted Answer

Average acceleration is average acceleration = (1/T)∫₀→T A t(T−t) dt. So average acceleration = A/T [Tt²/2 − t³/3]₀→T = A/T [T³/2 − T³/3] = AT²/6.