[HideousKojima]

The parts of a ship that thrusters are directly attached to experience acceleration first, the other parts that are further out from the thrusters won't accelerate immediately and if the acceleration is too sudden or extreme could be damaged or break off entirely.

And to answer your question in the other response, many thrusters have a minimum thrust, and even that minimum may be too much for the parts when deployed.

[martyvis]

By definition, as long as thrusters are firing, you are accelerating.

[chriswarbo]

Acceleration is defined as the change in velocity, and velocity is defined as the change in position (w.r.t. some inertial reference frame). There will always be some bending when thrust is applied at one part of a body; nothing is perfectly rigid.

As an extreme example, imagine a stick one lightyear in length: if we ignite a rocket on one end, firing perpendicular to the stick's length, then the other end cannot start moving for at least a year.