Vauhti kasvoi nopeasti.

• vauhti is the subject: speed, pace, or momentum
• kasvoi is the verb: past tense of kasvaa = grew / increased
• nopeasti is an adverb: quickly / rapidly

So structurally it is:

subject + verb + adverb

Because it is the subject of the sentence, and subjects are typically in the nominative in Finnish.

The nominative singular form is the basic dictionary-like form of the noun, and here that form is vauhti.

Kasvoi is in the past tense (often called the imperfect in Finnish grammar).

It is the 3rd person singular form of kasvaa.

• kasvaa = to grow, to increase
• kasvoi = grew, increased

So the sentence describes something that happened in the past.

Because Finnish does not need a separate pronoun here.

English often says it increased quickly or the speed increased quickly, but in Finnish the noun vauhti already serves as the subject, so no extra pronoun is needed.

Also, Finnish often leaves out subject pronouns when they are unnecessary.

Because nopeasti is an adverb, while nopea is an adjective.

• nopea = fast
• nopeasti = quickly

In this sentence, the word describes how the increasing happened, so Finnish uses the adverb:

• Vauhti kasvoi nopeasti = the speed increased quickly

If you used nopea, you would be describing a noun, not the action.

It is formed from the adjective nopea by adding -sti, which is a very common way to make adverbs in Finnish.

Examples:

• nopea → nopeasti = fast → quickly
• hidas → hitaasti = slow → slowly
• varma → varmasti = certain/sure → certainly

So -sti often works a bit like English -ly.

No. Vauhti can be used both literally and figuratively.

It can mean:

• physical speed
• pace
• momentum
• the rate at which something is progressing

So depending on context, Vauhti kasvoi nopeasti could mean:

• a vehicle literally sped up
• the pace of some activity increased
• momentum built quickly

Because kasvaa here is an intransitive verb.

That means the subject itself changes:

• Vauhti kasvoi = the speed increased

There is no direct object because nothing is being directly acted on.

Compare this idea with a more transitive expression:

• Hän lisäsi vauhtia = He/She increased the speed

Here, lisäsi means increased in the sense of causing something else to increase.

Yes. Finnish word order is fairly flexible, although Vauhti kasvoi nopeasti is the most neutral order here.

This version sounds like a plain statement:

• Vauhti kasvoi nopeasti.

Other orders are possible for emphasis:

• Nopeasti vauhti kasvoi.
  This puts more focus on quickly.
• Kasvoi vauhti nopeasti.
  This is much less neutral and would need a special context.

So the basic sentence uses the most natural, unmarked order.

To some extent, yes.

Finnish verbs often change their stem in different tenses, so learners need to get used to seeing forms that do not look exactly like the infinitive.

For this verb, it is useful simply to learn:

• kasvaa = to grow, increase
• kasvaa → present: kasvaa
• kasvoi → past: grew / increased

You do not need to panic if the past form looks less transparent at first. This is very normal in Finnish verb learning.

A rough guide is:

VAUH-ti KAS-voi NO-pe-as-ti

A few helpful points:

• Finnish stress is usually on the first syllable of each word.
• au in vauhti is a diphthong, somewhat like ow in cow.
• oi in kasvoi sounds roughly like oy in boy, but shorter and cleaner.
• Finnish vowels are pronounced clearly and consistently.

So the rhythm is very regular: VAUH-ti KAS-voi NO-pe-as-ti