In this case the person would experience 292Gs by the end of the 14 months, which should be enough to kill him/her but, considering that it would have taken 14 months for the environment to reach an acceleration instead of the environment suddenly accelerating at 292Gs that would cause the person to experience 292Gs, could the person have become acclimated to 292Gs over the 14 months.
Human tolerance of g-force is dependent on the magnitude of the g-force, the length of time it is applied, the direction it acts, the location of application, and the posture of the body as it experiences the force. As the human body is soft and flexible, a temporary experienced of high g-force may be tolerable where the constant application of it could be deadly. The risk of damage is exacerbated when vibration is also experienced, even in the application of low g levels, if the vibration occurs at the resonance frequency of organs and connective tissue.
G-tolerance can be trainable, however there is an element of innate endurance which some people posses and some do not.
The testing that has been done regarding human endurance for g-forces has been primarily focused along tolerance for vertical and horizontal g-force.
Positive vertical force, aligned with the spine, causes significant variation in blood pressure along the length of the subject's body which limits the maximum g-forces which can be tolerated. Positive g drives blood downward towards the feet. Resistances to this varies and your average person can handle about 5g while riding a roller coaster before passing out. Subjects provided with specialist gear and training (e.g. aviators/astronauts) can be expected to manage sustained periods of 9g.
Positive vertical g-forces can cause some pretty nasty side effects, especially relating to the eyes and the brain which include; - Grey out - the loss of color in sight. Reducing g-force will reverse this. - Tunnel vision - loss of peripheral vision. - Blackout - loss of vision entirely while still conscious. - "G-LOC" - loss of consciousness. - Death
Negative vertical g-forces, where blood is pushed towards the brain, have a far lower resistance level. the limit here is typically -2/-3g and can cause a condition called red out where vision takes on a red hue. Negative g can cause serious damage like brain swelling or bursting under the added blood pressure.
The human form is WAY better at withstanding g-forces perpendicular to the spine. this is why astronauts are seated, facing towards the direction force will be applied from during take off. Even untrained people can withstand 20g for 10 seconds or 10g for 1 minute in this position while conscious. The record for survival in this position belongs to a man named John Stapp who experienced a top g-force of 46.2 and sustained more than 25g for at least 1.1 seconds while riding a rocket sled at 632 mph - however the testing left him with life long damage to his sight. Doing the math, for the moment he experienced 46.2g, his 168-pound body weighed the equivalent of over 7,700 pounds
What all this means for the person in your scenario.
Blood Pressure - At sea level, or 1 G, we require 22 millimeters of mercury blood pressure to pump sufficient blood up the foot or so distance from our hearts to our brains. In 2 G's, we need twice that pressure, in 3 G's, three times, and so on. Without outside help or internal modification, they are going to top out at 4/5gs because their heart will be unable to create the pressure to continue pushing blood upwards toward the brain. With a specialized suit similar to what a fighter pilot wears, with air bladders to constrict the legs and abdomen during high G's to keep blood in the upper body, as well as training your subject could be pushed to withstand up to 8/9g. That said, this is based on experimentation done for limited amounts of time.
Weight - As Gs increase, your effective body weight increases. There's a question of what the max weight a person could handle moving around, even 'just' an extra 200lbs is going to put a lot of stress on your subject's joints. Humans start having severe difficulty with mobility to the point of debilitation around 400-500 lbs. while some of that is a size issue, it is also that their body's frame and muscles can no longer support the weight required in order to maintain movement.
My math is a little fuzzy but I would see the g-force increasing as below if starting at 1g and increasing by 50% every 30 days.
1g -> 1.5g -> 2.25g -> 3.375g -> 5.06g -> 7.591g -> 11.386 -> 17.079 -> ect.
Looking at NASA astronaut requirements, they must be between 58.5 and 76 inches in height. Astronauts must also maintain a healthy weight, proportional to their height. Lets split the difference and take the median height of 67.25 inches or 5.6 feet tall. Assuming a male test subject with a medium frame we'll call the expected weight 145lbs. Making these assumptions, we can expect the subject's effective weight to increase along side the gravity as follows:
1g -> 1.5g -> 2.25g -> 3.375g -> 5.06g -> 7.591g -> 11.386 -> 17.079 -> ect.
145 -> 217.5 -> 326.25 -> 489.375 -> 734.0625 -> 1101.09375 -> 1651.640625 -> 2477.4609375 -> ect.
So, based on data available, it's reasonable to think with that slow increase of g-force, that your subject could withstand up to 7.561g provided training, equipment and a slow increase of pressure. However, they would not be able to be mobile and functional at the effective weight of 1101.09375 lbs that would come with that g-force. Even at 5.06g and 734.0625 lbs they're really going to struggle. Your scenario doesn't specify what they would be doing during this period but I would expect they would need to be mobile for self care at the very least. With that in mind, I think that your test subject would begin to struggle as gravity approaches 2.25 and they would probably top out at 3.375 before becoming increasingly immobile and probably expiring from an inability to care for themselves rather than from the g-forces experienced.
could the person have become acclimated to 292Gs over the 14 months?
Based on my math and understanding, no.
Consider this simple analogous experiment. Suppose we strap a backpack on you, and every month we put lead weights in the backpack such that the combined weight of you plus the backpack increases by 50% each month. To keep round numbers, let's say you weigh 200 pounds.
So January the backpack is empty.
February we add 100 pounds of lead weights so you plus backpack equals 300 pounds. That would be hard to carry around, but you'd probably manage.
March we add and 150 pounds for a total of 450 pounds. I imagine that would be tough, and the fact that you had a month of practice with 300 pounds might help, but I doubt it would make it easy.
April we bring the total to 675 pounds. Do you think your practice with 300 and then 450 pounds would make this easy?
May we bring it up to 1012 pounds. (We'll give you a break and round down to the nearest whole pound.)
June you're at 1518 pounds.
We're only 6 months in and already I think you would be barely able to crawl. I doubt you'd survive 14 months. Would having the months of practice help? Maybe, but I sincerely doubt that any amount of time practicing carrying around 1000 pounds would make it easy to carry 1500 pounds.
Feel free to try the experiment. See how much the practice helps.
And bear in mind this is way easier than what you're postulating. At least with the backpack you could sit down and lean back, or lie on your back, and get a break. With G forces, the weight would always be all over you.
There are limits to the effectiveness of exercise and strength training. Try to increase the number of, say, push-ups that you can do even linearly. Like do one more push-up every day. So if today you can do 20, do 21 tomorrow, 22 the next day, 23 the next day, etc. Does it follow that if you kept up this program for five years that you would be able to do 1800 push-ups without taking a break? No. That's not how the human body works.
Just nope. Under 292g your body would weight 20 000 kilogrames, and your bones would break under your own weight. Even lying on floor, you would be flattened by forces much more deadly than road roller (road rollers weight ~12000 kg).
Your remains wouldn't be recognizable as human - it will be just very thin layer of organic matter.