Well, technically 'fast' here is an adverb that has the same form as the adjective (most dictionaries list adverbial fast alongist with the adjective), but I agree that 'quickly' should be accepted too.
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Apparently the word быстро is the origin of the French word "bistrot" meaning a small restaurant /café.
Wiki extract: The word derived from the Russian bystro (быстро), "quickly". It entered the French language during the Battle of Paris (1814). Russian officers or cossacks who wanted to be served quickly would shout "bystro."
This is a great way to help remember быстро, but FWIW, Wikipedia currently says "This etymology has been discredited by some French linguists, as there is no attestation to the occurrence of this word until the end of the 19th century." Other sources give other possible origins for "bistro": a word in the Poitou dialect which means a "lesser servant," bistouille or bistrouille which is a beverage, or bistraud: "a little shepherd." But apparently no one knows for sure.
Russian word order is flexible and allows some variation. If you want to make a generic statement, Дети быстро растут is more common (where "grow fast" is a single statement you want to make about kids). If you stress that children grow at a very high rate, you may as well move the adverb to the end of the sentence. Since both interpretations make sense, we accept both.
Numerous results from a context search say that it means both grow and grow up (when applied to children):
The idea that children grow physical but change in no other way is absurd. The English "grow up" means that the children get bigger, learn more, change in attitude, and hopefully become wiser as they progress towards adulthood.
It the sentence simply means what annika_a suggest, then you'd end up with a bunch of 2-meter tall 1-year-olds. That is simply a preposterous and ridiculous sentence. If that translation is valid, then it ought to be changed to a verb meaning "to grow up" as the English verb intends.
(There is only one person in the world I can think of who fits this definition.)
Both forms are correct, but they mean different things:
- Расти́ ‘to grow’ (3rd pl. расту́т) means ‘to become bigger/more mature’,
- Расти́ть ‘to grow’ (3rd pl. растя́т) mean ‘to let someone/something become bigger/more mature’.
- Де́ти расту́т ‘The children are growing’
- Де́ти растя́т цветы́ ‘The children are growing flowers’.
Расти́ть/растя́т describes an action directed to some outer object, расти́/расту́т describes an action directed at oneself.
Because 'children' is plural, so it need to be used with the plural verb form (grow). 'Grows' is a singular verb form, you'd use it with singular nouns (the child grows fast).
I believe it's not... :?
I'm not sure, different languages mark stressed syllables differently, but I can't tell much about the Russian stress, sorry. But this sentence definitely has the correct stress.
She's actually stressing быс, бы́стра.
The stress is not the same in different languages. For example, in Russian, /ə/ only exists in unstressed syllables. So, when Russian speakers hear /ə/ in other language, we might think it's unstressed even it's in fact stressed. Just because we're used to the fact /ə/ is unstressed.
I see you're from Brazil. If your native language is Portuguese, then you might be used to hearing Ы /ɨ/ as an unstressed variant of E. For example, in Portugal 'descrever' is pronounced like дышкрывэр (although I think it's pronounced without Ы in Brazil, so this makes my reasoning weaker...). If you're only used to hearing /ɨ/ in unstressed syllables only, you might mis-hear syllables with stressed /ɨ/ as unstressed.
Stress is actually quite a complex thing, not all the languages stress the words exactly in the same way, so it might take time to learn other language's stress patterns. Don't let this discourage you! :)
Unless, of course, they're adhering to something:
CLUELESS OLD #1: Why are those kids just standing there staring at their phones? CLUELESS OLD #2: Maybe they're growing fast. CLUELESS OLD #1: Don't you mean quickly? CLUELESS OLD #2: Nope. Have you seen them move in the last half hour? CLUELESS OLD #1: Uh-uh. That's why I asked. CLUELESS OLD #2: They're probably stuck fast by now. Feh! CLUELESS OLD #1: Don't you mean meh? CLUELESS OLD #2: No. I mean SHUT UP! Fast!