Not sure what you mean by "Shifting" into 2nd. There is nothing to shift. The transmission is a CVT, which works on two pulleys that vary in diameter, so it should be a smooth acceleration. There are some "Dogs" that can get worn on the primary pulley (the one on the motor). Maybe look for some binding on either of the pulleys.
If it was the belt, I would think that it just would not drive. Depending on the hours and how its been used, it might be time for a belt change regardless.