1995 Mercury Cougar Not really accelerating right.

Hi, I am having accelaration problems with my car. When I start it, it runs good but when I go to put it into gear it will move but it moves really slow for about 3 or 4 mins then it picks up a little but won't go over 25 or 30 miles per hour. If i'm at a stop sign and go to take off I can put the gas to the floor and it will only go about 5 mile or 10 miles per hour. I replaced the fuel filter and it doesn't really run any better than it did. Maybe kicks into gear a little faster but not too much. Is this my transmission going or something else? Please help. I don't know what to do! Thanks!