impulse drive is typically described as the slower-than-light drive
available to Star Trek ships. However, it is not too unusual for
impulse drive to exceed light speed, and a third propulsion system
exists: Maneuvering thrusters.
Impulse drives can throw around enormous amounts of momentum, even correcting for mass-lightening effects. Estimates for acceleration vary; however, it is clear that a capital ship's impulse engines can typically produce many giganewtons of thrust, which - with substantial mass-lightening - translates to 1,000+g easily. Impulse craft are sometimes seen reaching significant fractions of lightspeed within moments.
The sole effective limitation of impulse in sublight terms appears to be maneuverability, rather than sheer acceleration.
Maneuvering thrusters are intended for fine work. These appear to be classic Newtonian rockets, limited to low thrust, presumably no more than 1-10 g at the most.