G-V, speed - g relationship, is more by inference than exact value.
A very, very simple view of CS 25;-
A value of g is chosen - a structural limit. The aircraft response to the gust model is checked for a range of speeds, reducing until an acceptable compromise if found - the speed at which g is within the structure limit.
A similar assessment is made for low speed margin, with speed increasing, the result of the two being the turbulence speed or range of speeds. As per #28.
Whether this indicates a V^2 or linear relationship with force depends on the equations - a simple view might favour V^2.
The thread question relates to the effect of turbulence, presumably relating to comfort.
Comfort is subjective, an individual assessment. What is rough for a passenger could be a non event for the crew. Similar assessments might depend on aircraft type, or differences in structure and materials. At least one type that I flew had different responses between the cockpit (and rear cabin), and the centre section being least affected (flexing bent-banana mode), and again different modes - sway vs bounce which can affect people differently. And then there is roll …
Irrespective of the degree of comfort, passengers appear to favour a safe arrival, then being able to share their ‘horrific’ experiences, than to suffer physical harm or even not to arrive at all.