The most relevant explanations for the student's observations in this investigation are:
A. The food coloring moves faster in hot water.
Hot water has more kinetic energy than cold water, which means the molecules in the hot water move faster. This increased movement can help the food coloring disperse more quickly.
D. The food coloring is less dense than the cold water.
If the food coloring is less dense, it will rise and spread out more in the hot water, making the movement more noticeable.
The other options do not apply to the scenario:
B. The food coloring moves slower in hot water. (Incorrect - it moves faster in hot water.)
C. The food coloring is denser than the cold water. (Incorrect if it disperses faster in hot water, indicating it may be less dense.)
E. The food coloring separates into two different colors. (Not relevant unless specifically observed, which isn't mentioned.)
F. The food coloring increases the temperature of the water. (This is not correct; the food coloring will not significantly affect the overall temperature of the water.)
So, the correct selections are A and D.