Thanks R0J0hound . newt 99Instances2Go for your input and ideas. I think i managed to solve it finally. Or at least as close as I could.
Speed and acceleration is based on distance now, and it works great with touch taps and clicks also. If you click somewhere it will accelerate towards the distance based max speed, then slow down after it passed that threshold.
Updated capx if you want to take a look at how I solved it.
https://dl.dropboxusercontent.com/u/20560446/Scirra/smoothchase.capx
sprite turns blue when accelerating and red when decelerating.