"Free education and health care are among the other impetus". Here the subject is plural, and I want to use it with impetus. However, impetus is uncountable. What is the correct form of that sentence?
Impetus is countable. You can say "an impetus for ..." and have it sound perfectly reasonable. You can't do that for uncountable nouns, like "I'm looking for a furniture for my room" or "I just learned an interesting information."
There is a reason that you don't often see the plural. The Latin plural of impetus is impetus, like all fourth-declension Latin nouns ending with -us. This plural was used in English back when most educated English speakers knew Latin. We no longer use this plural (it was always quite rare), but we haven't replaced it with the regular impetuses, and impeti is just really, truly wrong. This means that impetus is in practice a singulare tantum — a singular noun that doesn't have any plural.
So what should you do? You could replace it with a synonym (maybe motivation). Or you could rephrase the sentence to use impetus in the singular, sort of like an uncountable noun:
Free education and healthcare are part of the impetus,
Free education and healthcare contribute to the impetus,
"Impetus" is usually used in the following structure
- ___ gave Impetus to ____
- ____ received Impetus from _____
So there aren't many ordinary cases where the plural "impetuses" is required
For example, "Free education and healthcare gave great impetus to the development of the nation"
Even "Free education and healthcare also gave new impetus" is correct provided context is supplied elsewhere
The way you've used it is rather clunky.