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Originally Posted by Nevadaref
If you really want to discuss this, I believe that you are incorrect. I believe that the average speed is the same if the object travels in a two-dimensional plane or if it makes a parabola, due to the force of gravity.
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A parabola is motion along a "2 dimensional" plane (a plane is 2D by definition so there's no other type) and it describes the vertical flight of an object as a function of time with zero drag (no atmosphere) and does factors in the force of gravity.
I'm not sure what to make of the rest of your post.