Here's the thing
m*(v1-v2) = m*a*(t1-t2)
So you get Change in velocity = Acceleration * change in time, basic definition of velocity and acceleration.
So while you want to include acceleration, your basically already did because velocity accounts for it. The thing your doing is transforming velocity into acceleration by its basic definition. So acceleration doesn't add anything to the situation. The reason is your adding in time, so it all equals out. The math there proves it, your saying.
m*deltaV = m*a*deltaT
So there EQUAL. Meaning acceleration can't add anything more to the system because its equal to the other side. You can't just throw acceleration in. Because there is no other term there. There equal.
Yes, and I was agreeing with you.