Li agis rapide.

Because rapide is an adverb, and adverbs in Esperanto end in -e.

Here, rapide describes how he acted, so it modifies the verb agis.

• rapida = quick, fast as an adjective
• rapide = quickly, fast as an adverb

So:

• Li estas rapida. = He is quick.
• Li agis rapide. = He acted quickly.

agis is the past tense of the verb agi.

Esperanto verb endings are very regular:

• -i = infinitive → agi = to act
• -as = present → agas = acts / is acting
• -is = past → agis = acted
• -os = future → agos = will act
• -us = conditional → agus = would act
• -u = imperative/jussive → agu = act!

So ag-is literally shows:

• ag- = the idea of acting
• -is = past tense

Li means he.

It is the third-person singular pronoun for a male person.

Some related pronouns are:

• mi = I
• vi = you
• ŝi = she
• ĝi = it
• ni = we
• ili = they

So in Li agis rapide, li is the subject: the person who did the acting.

Yes, to some extent. Esperanto word order is fairly flexible, although some orders sound more neutral than others.

The most neutral version is:

• Li agis rapide.

But these are also possible:

• Li rapide agis.
• Rapide li agis.

All of them mean roughly the same thing, though the emphasis may shift a little.

Since rapide is an adverb and there is no object here, the sentence remains clear.

Normally, Esperanto does use an explicit subject, because the verb ending does not show person.

For example:

• agis could mean I acted, you acted, he acted, they acted, etc., depending on context.

So Li agis rapide is the normal clear sentence.

You might sometimes see the subject omitted in special contexts, such as notes, diary style, poetry, or when the subject is extremely obvious, but that is not the standard beginner pattern.

Because there is no direct object.

The accusative ending -n is usually used for a direct object:

• Li legis la libron. = He read the book.

But in Li agis rapide, there is only:

• li = subject
• agis = verb
• rapide = adverb

No noun is receiving the action, so no accusative is needed.

Also, adverbs like rapide do not take -n here.

Not exactly.

• agi means to act, to take action, to behave
• fari means to do or to make

So Li agis rapide means he acted quickly, not necessarily that he did something quickly in the broadest possible sense.

Compare:

• Li agis rapide. = He acted quickly.
• Li faris tion rapide. = He did that quickly.

In many cases agi has a sense of behavior or action-taking, while fari is more general.

A simple pronunciation guide is:

• Li → lee
• agis → AH-gis
• rapide → ra-PEE-de

A few useful points:

• Esperanto stress is almost always on the second-to-last syllable
• so agis is stressed on A
• and rapide is stressed on PI

Also:

• g is always a hard g, as in go
• e is a clear vowel, not silent

No. Rapide means quickly or fast.

If you want soon, Esperanto usually uses baldaŭ.

So:

• Li agis rapide. = He acted quickly.
• Li agos baldaŭ. = He will act soon.

This is a useful distinction, because English learners sometimes connect quickly and soon, but Esperanto keeps them separate.

Yes, often it can.

Depending on context, agi may mean:

• to act
• to take action
• to behave

So Li agis rapide could mean he took action quickly, or he acted quickly in a situation. The exact nuance depends on context.

If you specifically want behave, Esperanto also has konduti in some contexts, but agi is a common general verb for acting.

Not exactly.

• Li agis rapide. = He acted quickly.
• Li estis rapida. = He was quick.

The first sentence focuses on the action and how it was done. The second focuses more on his quality or state.

So they are related, but not identical. Esperanto makes the same adjective/adverb distinction very clearly:

• rapida = quick
• rapide = quickly