According to economics, what determines the worth of a dollar of fiat currency?

You can use any economic jargon you want without explaining it.

Also, do not include in your explanation anything relating to outside countries. Assume that there is a planet on which there is only one country, and that one country has fiat currency.

I am really interested in this, and appreciate any help understanding this. Thanks in advance!

The value of a fiat currency is determined, when all is said and done, by people's willingness to accept it as payment for goods and services. That's it, nothing more and nothing less than people's faith in its purchasing power. You accept an essentially worthless piece of paper as payment for your labor because you believe that King Soopers will accept those pieces of paper when you go to buy groceries. The currency gains/loses value as people accept fewer or demand more of it as payment for the same goods and services.

Supply and demand. If the supply of money is increased, its worth less. If it's decreased, it's worth more. If peoples demand for cash balances increases, it's worth more, and if it decreases, it's worth less.