It is because of the heat in the hot water. Being hotter, the atoms have more kinetic energy, which also means the atoms are moving faster. Thus, the atoms in the coffee grounds and the atoms of the water in the hot water will collide a lot more than in the cold water, moving the coffee around the hot water a lot faster than in the cold water.
Good luck, Zain. I hope this helps.
The brown color is caused by diffusion. This means that the brown coffee molecules are being dispersed into the water.
When the water is hotter the water molecules move faster, because heat means more kinetic energy. Therefore the water molecules collide more frequently with the coffee molecules causing the coffee molecules to diffuse faster into the water.
Colder water means less motion and less collisions, and therefore slow diffusion.
For another example, sugar dissolves much slower in cold water than hot water.
In hot water the molecules are moving much faster, than in cold water.
It's because of diffusion. In hot water the color diffuses much quicker and spreads quicker as well since the molecules are moving so fast but in cold water the molecules are not moving as much and causes less diffusion.
When water is hot the molecules are moving much faster, than in cold water, therefore it is faster for coffee to touch molecules in order to disperse, in cold water it is slower as the molecules aren't moving as fast.