It would depend on the amounts of water and sugar
Yes, sugar can dissolve in a clear glass of cold water without stirring, but it will dissolve more slowly compared to if the water were warm. The process can be accelerated by stirring or heating the water.
You can increase the temperature of the water.
by heating the water slowly and by stirring using a spoon, you can dissolve salt and sugar.
What temperature is the tap water? A little will dissolve in room temperature tap water, but if you raise the temperature of the water more sugar will dissolve. If you boil the sugar, it will break down into two simpler sugars and won't precipitate when the water is cooled.
This depends on: - mass of sugar - granulation of sugar - volume of water - stirring (and intensity of stirring, stirrer type) - type and geometry of the beaker - exact temperature of water
Stirring makes it faster for the sugar to completely dissolve in the tea.
Vinegar is usually a solution 9 % of acetic acid in water. The solubility difference of sugar between water and vinegar is not significant at equal temperature, granulation of sugar and volume, without stirring.
That depends on the relative quantities of sugar and water, the water temperature (more definitely than merely "cold"), and any agitation (stirring).
The solubility of sugar in water increases with temperature. At 20°C, 300g of sugar can dissolve in water, while at a higher temperature like 80°C, more sugar can dissolve. The exact temperature at which 300g of sugar will dissolve in water depends on the water temperature and the saturation point of sugar in water at that specific temperature.
These effects are the same when dissolving anything into anything. Stirring, or motion, is the key. Stirring plays a role because it is motion in the solvent at the macro level. The temperature of the solvent (water) plays a role because the higher the temperature the more motion in the volume at the molecular level.
Sugar can typically dissolve in one cup of water as long as the water is warm or hot. Stirring the water also helps to fully dissolve the sugar more quickly.
Factors that cause sugar to dissolve faster include increasing the surface area of the sugar (finer crystals dissolve faster), stirring or agitating the solution, raising the temperature of the solvent (hot water dissolves sugar faster than cold water), and increasing the concentration of the solvent (higher concentration can dissolve more sugar).