What affects the rate of filling the Power Bar?

Naturally I want to fill the Power Bar as fast as possible, and from just the basics I can see:

• The bar seems to fill when picking up coins
• There are purchasable upgrades, which increase the rate that it charges

I'm most curious if the 2x and 3x coins fill it at 2x or 3x the rate, if the amount of "points" to fill it are always the same, and similar nuances like that.