Check the mechanical action of the brakes. Squeeze the brakes, one at a time, before starting to ride. The brake lever should move firmly but smoothly to engage the brake, and not display any sponginess or extra give when the brake is in contact with the rim. You should be able to push the bike forward with the brake engaged without the wheel rotating. Finally, spin each tire by holding up the bike and make sure that the brakes aren't rubbing against the rim when the brakes are off.