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There are a couple of things that can make the sugar dissolve into the iced tea faster. One is to stir the tea vigorously after you add the sugar. In order for the sugar to dissolve and diffuse, the larger sugar molecules have to collide with and find spaces between the water molecules.
Using granular or powdered sugar instead of sugar cubes or lumps will make the sugar dissolve faster, because adding the sugar in the form of smaller particles allows the liquid to make contact with all of the sugar molecules more quickly.
The best way to dissolve the sugar for iced tea is to first dissolve the sugar in a small amount of hot water, and then add that liquid to the iced tea. Hot water has more kinetic energy than cold water, meaning that the molecules are moving around faster and they also have more space between them. The faster they move, the more frequently the water molecules will collide with the sugar molecules and dissolve them, and the additional space between the water molecules gives the larger sugar molecules a place to go as they dissolve.
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