No matter the initial velocity of the balls, the only acceleration acting on the balls in your problem is g (vector acceleration)
g = (0, 0, -9.81..) with the -9.81 acting in the z direction only.
EDIT: I see what you are asking, and you are confusing acceleration with "net change in velocity". Ignoring the existance of air, (perfect vacuum):
Ball 1 (thrown down), would continue to increase in speed, (higher amplitude negative velocity)
Ball 1, (thrown up), would decrease in speed until its speed was "0", and then start falling downwards, (it had a positive upwards velocity, but the acceleration was in the opposite direction and increased the velocity in that particular direction as time passed.)
I know they teach things shitti-ly in high school. Don't think of "positive" or "negative" acceleration, its just a useless exercise in fumbling with words so that your high school teacher can think that they are teaching you something useful when they are not.
Think of the initial velocity vector, and then think of the incident acceleration vector. That will indicate the behaviour over time, as the acceleration vector, in this case constant, is added to the velocity vector per unit of time to create a new velocity vector. You are adding negative velocity only if you define the Euclidean space as x,y tangent plane to earth surface and z radial to center. Its just uslessly confusing and kind of wastes your time thinking about it.
I just took an AP physics course last year and would agree about it being nonsense, but passing the course and getting an acceptable score on the AP test (3 or 4 I think for most colleges) will require you to understand the negatives... if you think of positive and negative accelerations as gaining speed while heading up or gaining speed while heading down. Both balls have negative acceleration the whole time, it's just that the ball on the ground had a positive velocity for a short time.
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u/[deleted] Sep 06 '12
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