This Hebrew word (here in transliteration) bears no relation to the English word spelled the same way. It does not mean "somewhere in the distance," but instead, simply "dust."
I am a firm believer that we should never teach anything that needs to be unlearned at a later time. Most of us agree with that notion in principle, excepting maybe tooth fairies and Elijah's visit to the seder table, but in practical terms, we go out of our way to mask our discomfort with death by creating misleading euphemisms. One of them is some variation on "eternal sleep." We do no one a favor (especially children, who tend to be very literal) by inferring that one of these days bedtime will be permanent.
I make something of an exception for this phrase in the Amidah –"y'sheinei afar." While most English translations, including the one in our siddur, render "those who sleep in the dust," I suggest that it really means "those who sleep as dust." Instead of being meant euphemistically, it is meant quite literally.
Dust is perhaps the most inanimate of all physical substances. Though insubstantial, it will settle and remain stationary until something comes to disturb it. If you want proof, take a look under and around your computer (as I had the misfortune to do recently). Dust will accumulate with absolute lethargy until a puff of air or a rag comes along to disturb it. It is for this reason that tradition affirms that God used dust from the four corners of the earth to create the first human being, shaping it into form and then breathing life into it. Before that animating breath, that first earthling was without potential of life, just like the scattered dust it was.
When we die, our physical bodies return to the dust from which they were created. Even our ancient ancestors (who were much more direct about these matters) understood the finality of death. Yet their faith – and ours, if we merit it – is that God has promised to establish, sustain and fulfill a commit to restore life to the dust of that first earthling from which each of us is created.
After reciting the dependability of God's healing and life-affirming power, we are still forced to admit the inevitable: death is the destination of every life. Yet we insist that even when any one of us returns to the unmitigated sleep of inanimate detritus, God's power is to restore our life. As is God's promise.