Let's define "smooth driving"

[Gmen]

What do you think is smooth driving?

Here's two of my ideas:

1) Always try to have as little acceleration as possible (either forward/backward for gas/brake or left/right for steering) as possible. That's quite safe I think - no acceleration, no force felt by the passengeers

2) Always try to have as little derivative of acceleration (da/dt=d^3x/dt^3) as possible.
I came up with this idea thinking of myself standing on the subway. When the train starts to accelerate, I adjust forces on my hands and feet that make me steady. Now, if the acceleration changes a little, indeed I am able to manage these changes. And if the change is steady, I can even anticipate it. Obviously this is done for a very short time, as having a constant increase of acceleration makes x(t)=ct^3.
If the train driver has to stop suddenly, the change is large and this is what causes the discomfort.

What's everyone's opinion on this.

 

[Jonathan Scott]

The derivative of acceleration is called "jerk": https://en.wikipedia.org/wiki/Jerk_(physics)
As explained in that article, passenger comfort primarily relates to minimizing the magnitude of jerk, but also to limiting acceleration to a level that will not cause discomfort directly from pressure or similar.