How should i analyse the motion of a bouncing basketball? at which points would it accelerate?

 when you push it and it hits the floor

when you are bouncing the basketball, it would accelrate after it hits the ground

The ball is always accelerating.  There is a downward acceleration due to gravity that is always there -9.81m/s².  When you apply a force pushing it down this downward acceleration is made larger so the ball goes toward the ground faster than just its free fall alone. When it hits the ground the ball will bounce back.  This is the ball behaving like a spring that is compressed and then recoils.  The ball's velocity changes directions due to contact forces with the ground so there is an acceleration upward but the negative gravity acceleration is still there, it's just that the upward acceleration due bouncing is larger at that point.  The bounce, and therefore the bouncing acceleration only lasts for a moment though and since gravity's acceleration never goes away, the velocity change to the ball is eventually overcome and it falls back to the ground.

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