question about ps and ps2

i was wondering since my regular playstation is not working very good any more, its not loading up my games alot of times, but i am thinking about getting a ps2 and i was wondering if i could use my ps 1 memory card in it because i am pretty far in this rpg i want to play and i heard you can play playstation games on a playstation 2 or do i need a new memory card and have to start over??