Playing with particles and emitters

For this assignment, I was tasked with creating paarticles of either fire, smoke, rain, or an explosion given a folder of assets. I decided to create fire by choosing an asset that looks like a fire and by making the colors change from blue to red to gray.

I wanted to figure out a way to have exponential velocity, so that the particles would clump together at the beginning and then move faster the farther apart it gets, because a normal fire usually has a bigger flame at the base that then gets smaller the more it separates, but I couldn't figure out how to do it that way.