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.