What's the relation between speed of an aircraft and takeoff distance? I'm making a tool that when given : weight of aircraft , takeoff speed , runway length and some other parameters , it analysis the takeoff performance and states whether using the brakes now is safe or not . So I'm looking for a mathematical relation between the takeoff speed and the takeoff distance to use it in my code . Based on the given speed I want to determine whether the runway length will be enough or there will be a hazard . Is there any mathematical formula for calculating the takeoff distance using takeoff speed and weight ?? or how do people calculate that ? I need any method . 
Any help is appreciated . Thanks
I think your question is regarding new aircraft under design and not for existing planes?

The dynamics of ground roll/stopping is governed by one equation:

$$m\ddot{x}=T-D-\mu(L-mg)$$

where $T$ is thrust, $D$ is drag, $\mu$ is friction coefficient, $L$ is lift, $m$ is mass and $g$ is gravitational accel. Since thrust, drag and lift are a function of airspeed (and spoilers + brakes + thrust reverser should abort occur), the most naive way is just to numerically integrate the equation twice to get the distance at time.

That being said, don't forget that takeoff distance and accelerate-stop distance must be considered with all engines operating and with the critical engine failed. $V_1$, assuming not limited by controllability, should be selected such that the two distances balance. Also keep in mind that a good portion of takeoff distance is rotating and accelerating to $V_2$ before 35ft with the critical engine failed. The previous equation does not account for that portion.