Я быстро иду к выходу.

Because идти / иду is the verb used for going in one direction right now.

• Я иду к выходу = I am going toward the exit now.
• Я хожу к выходу would not fit this situation well, because ходить usually means:
  • going habitually
  • going back and forth / around
  • going in no single clear direction

This is one of the most important Russian verb pairs:

• идти = to go on foot, one-way, at this moment
• ходить = to go on foot regularly, repeatedly, or in various directions

So in this sentence, иду is the natural choice.

Because the preposition к requires the dative case.

The dictionary form is:

• выход = exit

After к, it changes:

• к выходу = toward the exit / to the exit

So:

• к
  • dative

This is a very common pattern:

• к дому = toward the house
• к двери = toward the door
• к другу = to a friend

That is why выход becomes выходу.

In this sentence, к means toward or up to, not necessarily into.

So Я быстро иду к выходу means the speaker is moving in the direction of the exit.

This is slightly different from other prepositions:

• к выходу = toward the exit
• в выход would not be normal Russian here
• на выход can exist in certain contexts, but it has a different feel and usage

If you want the basic learner-friendly idea, think of к here as:

• toward
• up to

Because быстро is an adverb, and it describes how the action is done.

• быстрый = fast, quick (adjective, describes a noun)
• быстро = quickly, fast (adverb, describes a verb)

Here it describes иду:

• иду = I am going
• быстро иду = I am going quickly

Compare:

• быстрый поезд = a fast train
• быстро иду = I walk/go quickly

Yes, often you can.

Russian verb endings usually show the subject clearly:

• иду already means I am going

So Быстро иду к выходу is possible and natural in context.

Including Я can:

• add emphasis
• make the sentence clearer
• sound more explicit

So both are possible:

• Я быстро иду к выходу
• Быстро иду к выходу

No, Russian word order is fairly flexible.

The neutral order here is:

• Я быстро иду к выходу

But other orders are possible depending on emphasis:

• Я иду быстро к выходу
• К выходу я быстро иду
• Быстро я иду к выходу

These all sound slightly different in focus or style, but the core meaning stays similar because the case endings help show the relationships.

For a learner, the safest default is:

• subject + adverb + verb + prepositional phrase

So Я быстро иду к выходу is a very good standard version.

It can mean both, depending on context.

More literally, идти is about going on foot. So the sentence suggests the speaker is moving by walking.

In English, depending on context, you might translate it as:

• I am walking quickly toward the exit
• I am going quickly toward the exit

Russian often uses идти where English might simply say go, but the Russian verb still carries the idea of movement on foot.

Usually it means right now: the speaker is currently moving toward the exit.

However, Russian present-tense verbs of motion can sometimes refer to the near future, especially if the context makes that clear.

For example:

• Я иду домой вечером can mean I’m going home this evening

But without any future time marker, Я быстро иду к выходу is understood as a present action happening now.

Пойду is different from иду.

• иду = I am going / I am on my way now
• пойду = I will go / I’ll start going

So:

• Я быстро иду к выходу = I am already moving quickly toward the exit
• Я быстро пойду к выходу = I will go quickly toward the exit / I’ll head toward the exit quickly

In other words:

• иду describes the movement in progress
• пойду often emphasizes the start of movement or a future action

Because Russian has no articles like a or the.

Russian simply says:

• к выходу

Whether English translates that as:

• to an exit
• to the exit

depends on context.

In many real situations, к выходу naturally becomes toward the exit, because the exit is understood from the situation.

A natural pronunciation is roughly:

• Я = ya
• быстро = BЫ-stra
• иду = ee-DU
• к выходу = k VY-ha-du

Main word stress:

• бы́стро
• иду́
• вы́ходу

A rough full pronunciation guide:

• ya BY-stra ee-DOO k VY-ha-du

A small pronunciation note:

• к is pronounced together with the next word, so к выходу flows as one chunk.

Sometimes на выход exists, but it is not the same basic structure and not always interchangeable.

• к выходу = toward the exit
• на выход can sound more like to the way out / for the exit, and may appear in set expressions, commands, or specific contexts

For a learner, к выходу is the clearest and safest choice for toward the exit.

So if your goal is to describe physical movement in the direction of the exit, Я быстро иду к выходу is excellent.

It breaks down like this:

• Я = subject, I
• быстро = adverb, quickly
• иду = verb, am going / am walking
• к выходу = prepositional phrase, toward the exit

So the structure is:

subject + adverb + verb + direction phrase

This is a very common and useful Russian pattern:

• Я медленно иду к дому = I am walking slowly toward the house
• Он быстро идёт к двери = He is walking quickly toward the door

So this sentence is a great model for building similar ones.