You have to start in first gear, then switch to second and then finally third as you start up. If you are in 2nd or 3rd gear when you are starting from the stop sign, it will be a slow start.
It Sounds like it's running to rich try adjusting the mixture or rejetting the carb to normal size.
Because it's a moped.
I have a 2000 49cc Yamaha Jog. It gets to a pretty high speed I can hi 45 on it easily, but when taking off the thing barely moves it just rolls along. It does seem to speed up a bit quicker when giving it less throttle until it speeds up a bit then I can give it more. Once I hit about 20mph or a bit higher it seems to speed up and run great. It does however jerk a tiny bit sometimes at top speed also, and right after I start it if someone heavy tries to use it it dies a lot when trying to take off, but once it gets going it stops doing this but always accelerates really slow when I stop which makes it very difficult and unsafe at intersections when I am forced to stop and have to roll basically for a minute or more. Thanks for any replies if you need more info just ask.