To explain the observations made by the student in this investigation, the relevant options would be:
A. The food coloring moves faster in hot water.
This is because molecules in hot water have more kinetic energy, leading to faster diffusion of the food coloring.
D. The food coloring is less dense than the cold water.
This helps the food coloring to rise and spread throughout the water, but its relative density compared to the water would depend on the specific properties of the food coloring. Generally, food coloring is designed to mix with water, implying it does not greatly affect the water's density.
The other options do not correctly explain the observations:
B. The food coloring moves slower in hot water. (Incorrect, as explained above.) C. The food coloring is denser than the cold water. (Usually, food coloring is not denser than water.) E. The food coloring separates into two different colors. (This may happen with some types of coloring, but it's not a given and not relevant to this investigation.) F. The food coloring increases the temperature of the water. (The food coloring's temperature is lower than the hot water it's added to, and its effect on the overall temperature of the water would likely be negligible.)
Thus, the best explanations for the student's observations would be A and D.