The two formulas shown below are used to help understand the key components in calculating the take-off distance. The upper formula is used to calculate the distance required (s) to reach a specified speed (V) with a given acceleration (ā). Beneath the first formula is the formula to calculate that acceleration.
For an aircraft taking off, the acceleration is thrust minus drag. However, both of these forces will change as the speed changes, and so the acceleration will not be constant during the take off. Also, during the airborne part of the take-off, the laws of motion will be somewhat different, and the upper formula will change somewhat, but the distance required will still depend on the speed to be achieved and the acceleration.