SUVAT
Tommoutrie,
Although the factor seems to be "linear", it is applied to the total distance which already takes the v-squared into account. For example, if you oversimplify landing after WoW to a constant de-acceleration rate of say 'a', then distance to stop = 0.5*(initial velocity)*(initial velocity)* a
On reflection this is reasonable since a large 'a' gets the SLF pushed hard into the seat restraints, and without the help of draggy devices and/or reverse thrust, 'a' cannot exceed 1g. So a "linear" factor allows a more comfortable de-acceleration rate.
Now as to what factor is appropriate .....