Can power ups spawns be predicted?

Solution 1:

By how I've played, you usually get one during 500-650m and the second one is at 1000-1200m. Even further, you get into a mine, soon after you get out, there will soon be another power up. This is about how far I have gotten.I hope to get even further to find more power ups to improve this answer even farther.

Solution 2:

Power-ups appear fairly consistently - once you've gone 600 meters (without any frequency upgrades) without a powerup, one should appear. Failing to collect the power-up doesn't seem to affect the distance that the next one appears.

Power-ups can't appear above rope slides or during mine cart sections, but the distance traveled on those counts towards distance without a power-up and if you've reached the required distance in one of those areas the power-up should appear at the exit.

Gems and treasures always replace a power-up.

When using boost as your active power and power-up frequency are both fully leveled by coins: I find the best strategy is to only manually activate boost within a short window after the power-up spawn. Otherwise, you are likely to be boosting at the next power-up, making it extremely hard to collect.