Мне удалось пересесть на другой троллейбус, и до дома я доехал быстрее.

Because удалось comes from удаться, which is often used in an impersonal pattern:

• мне удалось...
• ему удалось...
• нам удалось...

Literally, it works like it succeeded for me or it turned out possible for me.

So мне is in the dative case, and it marks the person who managed to do something. Russian does not say я удалось.

A very common pattern is:

кому? + удалось + infinitive
= someone managed to do something

So:

Мне удалось пересесть = I managed to transfer / I succeeded in changing buses

Both can often be translated as managed to or was able to, but the nuance is a little different.

• мне удалось пересесть = I managed to transfer, with a sense that it worked out successfully, perhaps despite difficulty
• я смог пересесть = I was able to transfer, more directly focused on ability/possibility

Удалось often sounds a bit more like a successful outcome. It can suggest that things went in the speaker’s favor.

So in this sentence, мне удалось пересесть feels very natural if the transfer was important or not guaranteed.

Пересесть means to change from one seat/vehicle to another, and in transport contexts it often means to transfer.

So:

• сесть = to sit down / to get on
• поехать = to go by vehicle / set off
• пересесть = to switch to another vehicle

In this sentence, the speaker was already traveling and then changed to a different trolleybus. That is exactly the situation where пересесть is used.

With public transport, Russian often uses на when talking about getting onto or riding a form of transport:

• на автобус
• на поезд
• на трамвай
• на троллейбус

So:

пересесть на другой троллейбус = to transfer to another trolleybus

This is one of those patterns you largely have to learn as a usage habit. English speakers often expect in/into, but Russian commonly prefers на with transport in expressions like this.

It is in the accusative case, because it follows на with motion toward something:

• пересесть на что? → на другой троллейбус

Since троллейбус is masculine singular inanimate, its accusative form looks the same as the nominative:

• nominative: другой троллейбус
• accusative: другой троллейбус

So the form does not change visibly, but grammatically it is accusative.

It can suggest either, and in this sentence both ideas fit.

• another trolleybus
• a different trolleybus

Because the speaker is transferring, the basic idea is that they changed from the one they were on to a different one. In natural English, another trolleybus is probably the smoothest translation, but different is also part of the meaning.

До takes the genitive case, and дома here is the genitive singular of дом.

So:

• до
  • genitive
• дом → дома

The phrase до дома means as far as home / to home / all the way home, especially with verbs of travel such as доехать, дойти, добраться.

This combination is very common:

• доехать до дома = to get home by transport
• дойти до дома = to walk home / reach home on foot
• добраться до дома = to make it home

Because доехать is a perfective verb meaning to get as far as / reach by transport. It focuses on the completed result: the speaker reached home.

Compare:

• ехал = was going / was riding / went by vehicle, focusing on the process
• доехал = got there by vehicle, focusing on successful arrival

In this sentence, the important point is the result of the transfer: after changing trolleybuses, the speaker got home faster. That is why доехал is the natural choice.

Sometimes приехал домой is possible in similar contexts, but доехал до дома is especially natural when the emphasis is on reaching the destination by transport.

A useful contrast:

• приехать = to arrive
• доехать до... = to get as far as..., to reach a place by vehicle

In this sentence, доехал до дома highlights the completed trip from the current point all the way to home. It matches the idea of travel after transferring vehicles very well.

Russian word order is flexible, and it often reflects emphasis or information flow rather than strict grammatical necessity.

All of these are possible in principle:

• И до дома я доехал быстрее.
• И я доехал до дома быстрее.
• И я быстрее доехал до дома.

The version in the sentence puts до дома early, which helps frame the destination first. It can sound a bit like:

And as for getting home, I got there faster.

So the word order is natural and slightly expressive, not random.

Быстрее is the comparative form of the adverb быстро.

• быстро = quickly
• быстрее = more quickly / faster

Here it modifies the verb доехал, so it is an adverb, not an adjective.

So:

доехал быстрее = got there faster / rode there more quickly

In Russian past tense, singular forms agree with the gender of the subject:

• я доехал = if the speaker is male
• я доехала = if the speaker is female

So this sentence suggests that the speaker is male. If a woman were speaking, the second part would be:

и до дома я доехала быстрее

Also, in the first part, удалось stays the same because that construction is impersonal.

Yes. Both verbs present completed results:

• удалось пересесть = the transfer was successfully accomplished
• доехал быстрее = the speaker reached home faster

This makes the sentence sound like a sequence of successful completed events:

1. the speaker managed to transfer
2. as a result, the speaker got home faster

That is a very typical Russian way of presenting a finished chain of events in the past.