I was thinking of a problem on my own when I came upon an entirely new idea. Assume that a force(call it air resistance) acts on a body such that it opposes the motion of the body by an acceleration a. If the body is at rest, it doesn't act. I know that it is not possible but just assume such a system. Now, suppose you throw a ball upwards with considerable speed. Let us consider cases and analyse the motion of the ball. Case I: If a<g. The ball moves up with deceleration(a+g) and comes to rest and comes down with less acceleration (g-a) on it. Case II: a=g The ball moves up with fair deceleration 2g, comes to rest. Now, at the instant when it is at rest, air resistance doesn't act on the ball. But since gravity does, the ball starts coming down but air resistance pulls it up with same force and so, the ball just floats in air neither going up nor coming down. Case III: a>g The ball moves up with powerful deceleration (a+g) and comes to rest. Now, consider the instant when it is at rest. Only gravity acts on it and so, it tends to come down. But if it does come down for an instant, air resistance acts upon it pulling it upwards with acceleration more than gravity. So, just as the ball starts moving down, it is pulled forcibly upwards and hence, for an instant, tends to move up. Now, again, air resistance changes its direction(remember that it just tends to oppose the motion like friction), and begins pulling it downwards and gravity also pulls and so, the ball again starts falling down for a fraction of time. Finally, we can see that the ball never moves at all. My question is, am I right in this analysis of the motion of the ball? Because it seems vague and incorrect(for the third case).