This is an adverb. There are a lot of people who become confused with adverbs and adjectives. If the word is careful, this would be an adjective because it describes the person who is doing the action.
For example, if the sentence is about the driver, then the driver being careful makes the word careful an adjective. If the word carefully would be used, however, this is already an adverb because it describes how the verb is being done. This is precisely what an adverb is for. Take note that the adverb is normally used to provide a description of the verb while the adjective describes the noun.
