sensing distance of an obstetrical, to stop swing door

Have a question but, here is the idea of the project first.
Using a ping sensor to find the distance of an object.
the ping sensor would be mount at the edge of the door looking for objects.
when and object is detected at a set range the door will be stopped and not allow to open more.
note: that the ping sensor will be moving and a range of how close the door can get will be set.
question:
can a arduino be fast enough to do this calculation?
calculation being crunch the numbers coming from the ping sensor and stopping the door, via output a signal to the stop device, at a set distance.

New to the arduino but not to the avr/atmel world

Thank in advance for the help.

can a arduino be fast enough to do this calculation?

Yes anything that moves will be moving at the speed of a glacier as far as the processor is concerned.

Three concerns about the project.

  1. Getting the coverage of the area you want from a ping sensor
  2. Actually stopping the door.
  3. Wires to the swinging door to power the sensor is not good.