A method and systems for controlling a speed of a vehicle are provided. The control system includes an input device configured to receive a required time of arrival (RTA) at a waypoint and a processor communicatively coupled to said input device, said processor programmed to automatically determine a dynamically adjustable range for an autothrottle control using an RTA error and a speed control tolerance, the RTA error representing a difference between an estimated time of arrival (ETA) and the RTA, the speed control tolerance representing a tolerance range about the vehicle speed profile. The control system also includes an output device communicatively coupled to said processor, said output device is configured to transmit at least one of a thrust control signal and a drag control signal to a speed control system of the vehicle.