Acceleration describes how velocity changes. You can certainly have zero instantaneous velocity and non-zero acceleration.I have a point to make here, I dont deny that theoretically it makes perfect sense to say that acceleration exists in the absence of velocity,
in fact at zero velocity most equations would have negative acceleration.
OK, you can think of it that way. Gravity exerts a downward force on the ball, which produces a downward acceleration. It "retards" the ball on the way up, but that same force speeds the ball up on the way down.My point about the ball going up is simple, the earth continues to retard the ball even as it moves up and here the g acts as retardation.
The "retardation" is the acceleration of the ball. Perhaps you mean that the retardation/acceleration overcomes the velocity. (Sloppy terminology, but OK.)When the retardation overcomes the acceleration of the ball,
After reaching its highest point, the ball starts to move in the opposite direction. The acceleration, 9.8 m/s^2 downward, hasn't changed.the ball stops and thereby you would have the ball accelerating in the opposite direction.
Again, this is meaningless: What you call the "retardation" is the acceleration, which is downward. (Realize that "acceleration" in physics doesn't just mean "speeding up"--it refers to changing velocity, whether speeding up or slowing down.)Hence my point remains that at zero velocity, the acceleration of the ball would be equal to the retardation and the ball would stop, so acceleration here is discontinuous.