“So if a person goes on an airplane and it accelerates to whatever it’s supposed to accelerate to, time is going slower then?”
Yes!
Though note even a jumbo jet while traveling fast at say 550 mph (~ 0.15 miles per second) is nothing compared to the 186,000 m/sec that light travels. so it is not noticeable but it is real and even measurable! w/ atomic clocks.
look up “time dilation at low speeds” for a nice explanation with concrete numbers