The modernizing world is a vibrant, global society which gives and takes privileges to old and potentially new superpowers. (Incorrect word choice in the word modernizing)

As countries once thought to be third-world are advancing economically, politically and culturally, American citizens find their heart rates escalating to a deadly level when faced with the knowledge that their economy may no longer be the best in the world at some point in their lives. (Run-On sentence and there is not a fluid connection between the two thoughts, also be careful of hyperbole as it tends to detract from your point if not used well)

But is their worry justifiable? It is difficult to tell just how at risk the U.S. is of being pushed off its pedestal at this point in time or even how the country will be effected. (this is in direct contradiction from your first two sentence where you imply that it is a done deal. Also, don't start a sentence with but.)

It is certain, though, that America will need to adapt to this drastic change of scenery in order for its people to be truly at ease and maintain the American dream. (This conflicts with the previous sentence where you ask if it is true, you imply that it is not, yet here you state that it is a certainty).

to me it is an excellent beginning in the next few paragraphs develop the theme of your introductory as to the who what when ,where and why the US worries may be justifiable by comparing on a economic political and cultural scale in comparison to other countries