GearDown&Locked
I don't know for sure but I suspect both the speed relationship with time and with distance are non-linear.
I'm a great believer in K.I.S.S. and in this case you don't need complex integrals of ground speed to get distance - if you (or your computer) can calculate the expected time to V1 & VR for the weight and power settings, then you check your speed at those times - if your speed is below the projections you're running into trouble, but at least you know you have the tarmac left to stop. If the speed is at or above projections at those times then you're good to go.
This approach is inherently safer than measuring time to V1 - what happens in that case if acceleration is low? You could easily find yourself in a position where you don't have space to stop.