Interesting stuff. A bit of physics never hurt but...
Lets assume, for an airplane moving from 0 to Vr along a runway, the net force pulling the airplane forwards is constant and airplane mass is constant, so acceleration is constant. This is not going to be 100% correct, but given the speeds and environment it will be close enough for our purposes.
Unfortunately slim, it's nowhere near close enough. Reality is often much
worse than that. There are two important features that change along the take-off roll.
The first is the thrust developed by the propeller. The thrust developed by the propeller can easily fall to no more than 70% of its static thrust by the time you get close to rotation speed.
The second is the drag on the aircraft. The parasite drag, zero at rest, has often reached significant values by the time rotation speed approaches and it increases with the square of the speed.
These conspire together to mean that your acceleration falls sharply as you progress in the take-off roll. As a result, an aircraft that reaches 71% of its rotation speed half way down the runway may be nowhere near rotation speed by the time it reaches the end.
You also neglect the wind in your assessment. A headwind makes matters worse still. Imagine an aircraft that rotates at 60 knots taking off into a 25 knot headwind. It will reach an IAS of 30 knots almost immediately in the take-off roll, but has a very long way to go before it gets airborne.
The case you describe is the best possible case -- it's usually necessary to be much more conservative.
(BTW Leibnitz invented calculus first
)