Impulse drive appears to have little respect for traditional physics as understood today. It provides extraordinary accelerations, although extraordinary maneuverability is not established. Interestingly enough, impulse appears sometimes to be an FTL drive.
Season 1: "The Naked Now" - Any stellar debris from a red giant about to collapse all the way into a white dwarf could be outrun at "half impulse."
Season 2: In "Loud as a Whisper," half impulse is described as a velocity, rather than an acceleration.
Season 3: "Deja Q" - we have an "asteroidal moon" which the Enterprise imparts 92 m/s of delta v to in a short order with its tractor beam; needed is 4 km/s, which may theoretically be created by routing 147% of safe impulse power through the tractor beam for 29 hours. Unfortunately, it is the tractor beam circuits cannot handle this quantity, limiting its use for impulse engine analysis. The warp field is used to reduce the mass to 2.5 million tons. Dividing across, this suggests the original mass of the moon to be ~110 million tons, which would place the average force of the tractor beam over time as being no more than 4.16 billion newtons at 1.47 times normal impulse power to the tractor beam in the original estimate; however, we may also recall that the moon is very rapidly decaying into a collision orbit. At the most, this fast orbital decay represents a free falling mass at a radius of 7000 kilometers from an approximately Earth sized planet, which at an effective tonnage of 2.5 million tons, would experience a gravitational force of 224 billion newtons. GCS impulse engines therefore can exert a total force of at least 4.16-228 giganewtons, and can communicate a total realspace impulse of at least 435 trillion kgm/s. In "Allegiance," we see a close inspection orbit of a pulsar at 20 million kilometers. Acceleration must therefore exceed 1.44 m/s2.
The Borg, after dropping out of warp, crossed from Jupiter to Earth in an estimated 27 minutes. The Enterprise exits by Saturn, with an intended 23:14 intercept of the Borg vessel. Initial velocity is unknown, but it is reasonable to conclude that neither vessel was on track to overshoot Earth, and we may assume that the Borg vessel. Given Newton's equations of motion and the orbital dynamics of Earth, Jupiter, and Saturn, this would translate to roughly to 49-144,000g for the Borg cube and 134-331,000g for the Galaxy class starship. Unfortunately, this would involve speeds well beyond that of light.
In realistic (e.g., Einsteinian) terms, the time given to target at impulse appears faster than c in terms of average velocity: Saturn does not cross within 25 light minutes of Earth. This is mildly troubling, although possible from a dilated frame of reference, as in aboard a spaceship moving close to light speed. In order for time aboard the Enterprise to be sufficiently compressed to take 23:14 from Saturn to Earth, the average speed would be 0.95c or higher. Modeling the relativistic motion in detail, we arrive at an impulse per second that insists on the decidedly impolite range of something times 107-8 m/s2.
Season 4: The energy blobs of "Galaxy's Child." Detected moving at 2 million kilometers with sensors that are having "trouble getting clear readings past four thousand kilometers," they have an ETA of 10 minutes, 31 seconds, for an estimated velocity of 3,170 kilometers per second. If this course intercept, cited as being "at their current speed," refers to a constant acceleration intercept with the stationary Enterprise, then the blobs would have used an acceleration of 1024-2048g. "Night Terrors" sees the Enterprise using Bussard collectors while stationary, collecting a great deal of hydrogen and spitting it out for two minutes. "In Theory" - shuttles are more maneuverable than GCS. Inertial compensation is an absolute necessity at 0.1 impulse; this suggests somewhere greater than 50g for full impulse. Nacelles are used for impulse power, and shuttles have thrusters.
Season 5: In "The First Duty," Wesley and his flight teammates were flying close maneuvers at 80,000 kph (including sharp turns) when an accident happened. Being able to alter vector from 80,000 kph in one direction to 80,000 kph in a perpendicular direction in 1-10 seconds requires 450-4500 gees of acceleration. In "Relics," the Enterprise is orbiting 150,000 km outside a sun in a 200,000,000 km diameter Dyson sphere. 60% impulse power will get them out in 1 minute 40 seconds; this suggests FTL travel.