Learn Polish: Taksówka podjechała do barierki. - The taxi drove up to the barrier.

The prefix pod- adds the idea of approaching or coming right up close to a target. While jechać means to go by vehicle, podjechać means to drive up to or pull up. Adding this prefix also makes the verb perfective, meaning it represents a completed action.

Why do we need the preposition do here?

Motion verbs with the pod- prefix almost always pair with the preposition do (to) to introduce the destination you are approaching. The preposition do always forces the following noun into the Genitive case, which is why we see do barierki.

Why does barierka change to barierki instead of taking the usual -y Genitive ending for feminine nouns?

Generally, feminine nouns ending in -a take an -y ending in the Genitive case. However, barierka ends in -ka. Polish spelling rules state you can never write -ky or -gy, so the ending must soften to an -i, resulting in barierki.

What would the verb look like if the taxi was driving up (ongoing) rather than having completed the action?

You would use the imperfective equivalent, podjeżdżała. The verb used here, podjechała, is perfective, meaning the taxi has completely finished the action of pulling up to the barrier.