Under which conditions will sugar most likely dissolve fastest in a cup of water? a. a sugar cube with stirring at 5oc b. a sugar cube without stirring at 15oc c. sugar crystals with stirring at 15oc d. sugar crystals without stirring at 5oc

I believe the answer is sugar crystals with stirring at 15 degrees Celsius. 
Solubility is the maximum amount of a substance that will dissolve in a given amount of solvent at a specific temperature. There are two major factors that affect solubility are temperature and pressure. Temperature affects solubility of both solids and gases, but pressure only affects the solubility of gases. Increasing the surface area of solutes also increases the solubility. 

Particle exchange energy though elastic collision , hope this .