Polako popusti ovaj konop.

Polako is an adverb meaning slowly, gently, or sometimes easy/carefully, depending on context.

In this sentence, it tells the person how to do the action: not suddenly, but in a controlled way. With commands, polako often sounds like do it carefully or take it easy.

Popusti is the imperative form, used for giving a command to one person.

The dictionary form is popustiti.
So:

• popustiti = infinitive, to loosen / to let out / to slacken
• popusti = imperative, loosen! / let out!

So the sentence is directly telling one person to do something.

Yes. The subject is understood as you singular.

Croatian usually does not need to say the subject pronoun in commands, because the verb form already shows it. So:

• Popusti... = You, loosen...

If you added ti, it would sound more emphatic, but it is normally unnecessary.

This is about aspect, which is very important in Croatian.

• popustiti = perfective
• popuštati = imperfective

The imperative popusti usually suggests do this action as one complete act.
The imperative popuštaj would suggest keep loosening, be loosening, or do it repeatedly/continuously.

In a practical instruction like this one, popusti sounds like a normal single command: loosen this rope.
If the speaker wanted to emphasize a continuing gradual process, popuštaj could also appear in the right context.

Good question. Ovaj konop is the direct object, so it is in the accusative case.

However, for a masculine inanimate singular noun, the accusative is the same as the nominative. That is why it looks unchanged.

So:

• nominative: ovaj konop = this rope
• accusative: ovaj konop = this rope as a direct object

If it were a masculine animate noun, the form would look different.

It is in the accusative singular, because it is the direct object of the verb.

The full object phrase is ovaj konop. Even though it looks the same as the nominative, its function in the sentence is accusative.

Not usually. Popustiti konop more naturally means loosen the rope, slacken it, or let some of it out.

It does not usually mean completely releasing it from your hand.
So the idea is more like reducing tension, not necessarily dropping it.

Putting polako first is very natural in Croatian and gives immediate emphasis to the manner of the action.

So the sentence first tells you how to do it, and then what to do:

• Polako = slowly, carefully
• popusti ovaj konop = loosen this rope

Other word orders are possible, but this one is very normal and clear for an instruction.

Yes, konop is a normal word for rope or cord, especially in practical, physical situations.

Learners may also see uže, which can also mean rope. In many contexts they overlap, but konop often feels like a sturdy rope, line, or cord used for work, tying, sailing, climbing, and similar situations.

You would use the plural/formal imperative:

• Polako popustite ovaj konop.

In Croatian, the same plural verb form is used for:

• talking to more than one person
• speaking politely/formally to one person

So:

• popusti = singular informal
• popustite = plural or formal

It can be either, depending on tone of voice and situation. But the word polako makes it sound more controlled and careful than abrupt.

Compare:

• Popusti ovaj konop! = more direct, possibly sharper
• Polako popusti ovaj konop. = loosen it slowly/carefully

So polako softens the command a bit and adds the idea of caution.