how to calculate a negative acceleration?

Question

I\'m implementing the scrolling behaviour of a touch screen UI but I\'m too tired in the moment to wrap my mind around some supposedly trivial piece of math:

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Answer 1

A bit of non programming discussion about the car example.

First, I'll assume that the driver cannot cause the brakes to lock at speed.

The first thing (or maybe the second or third thing) most new drivers learn is that the natural tendency when braking is to hold the brake pedal at a fixed position. The result is a sudden lurch forward as the car goes from moving slowly to stopping. This happens because the brakes are transitioning from dynamic friction, where braking force is proportional to brake pressure, to static friction, where braking force is restoring the forward momentum of the car. this sudden jump in acceleration is unpleasant, and the new driver learns to feather the pedal at the very end of deceleration to stop.

This behavior masks another pecularity, but this can be noticed during normal acceleration in a manual transmission car. when accelerating (or decelerating), if the driver suddenly pops the transmission out of gear, all of the passengers will suddenly lurch forward. What is actually happening, is the accelerating force that was pressing them into the backs of their seats is suddenly removed, and they spring back to a neutral sitting position. A more comfortable way to drive is to gradually feather the clutch so the motive force of the engine is removed gradually.

In both cases, the more aesthetic driving style involves smoothing the acceleration, removing sudden jumps. This is basically another way of talking about continious second derivative. Almost any motion with this property will seem natural.