If a space ship launched into space continuously accelerates?

What is the acceleration? Without knowing exactly what it is you cannot work out what the speed will be after 30 days.

There are theories that the maximum speed is light speed.  I believe that it might be able for something to go faster but our molecular structure might not be able to withstand it.  Nevertheless, we  may not be able to detect it.

Acceleration is not a force - it is the result of an ubalanced force acting on a mass.  However, to find out how fast the ship would be going, you need to know the acceleration.  Suppose it is teh same as teh acceleration due to gravity ont he surface of teh earth (9.8 m/s^2).  Thirty days of constant 1 g accleration increases speed by:

  v = gt  = 9.8 m/s^2*(30 days*24hr/day*60 min/hr*60sec/min)

  v = 2.5x10^7 m/s  (5.7x10^7 miles/hr) or about 8% the speed of light

As the ship continues to accelerate, relativity becomes important so the ship's speed will approach that of light but never get to the actuial speed of light.  That;s assuming you have an almost infinite source of energy to power the ship.