What's the acceleration and absolute minimal RWY length for an A320 during take-off?
At takeoff weight of 78.9 tonnes and -20°C temperature (best case scenario), the A320 needs 2,250 metres (7,400 feet). (This includes the distance to reject a takeoff.)

As for the forces, you forgot to take into account the aerodynamic drag and rolling friction, both will slow down the acceleration.



This PDF from Virginia Tech explains the forces at work and the equations needed.