Is the word rápido the same in Brazilian and European Portuguese?

Yes

The word "rápido" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the "d" is typically palatalized, sounding like a "dj" ([dʒ]), and the vowels are more open and distinct. In Continental Portuguese, the "d" is dental (the tongue touches the teeth), and the unstressed vowels are more reduced or "closed," making the word sound much shorter and sharper.

Brazilian Portuguese

1. Ele é muito rápido no trabalho. (He is very fast at work.)
2. Preciso de um lanche rápido. (I need a quick snack.)
3. O ônibus passou muito rápido. (The bus passed by very fast.)
4. Você consegue ser mais rápido? (Can you be faster?)
5. Tudo aconteceu muito rápido. (Everything happened very fast.)

European Portuguese

1. Ele é muito rápido no trabalho. (He is very fast at work.)
2. Preciso de um lanche rápido. (I need a quick snack.)
3. O autocarro passou muito depressa. (The bus passed by very fast.)
4. Consegues ser mais ligeiro? (Can you be faster?)
5. Tudo aconteceu muito depressa. (Everything happened very fast.)