Everyone has heard the phrase, "Time flies when you're having fun." As simple as is seems, I believe this fully explains why time accelerates as we age. The question remains as to whether time is a constant, or if it really changes as we perceive it to.
Children constantly complain of being bored if they are not continuously engaged in some sort of activity. They have an inherent drive to learn, observe, touch and experience the world. This is why they experiment, sometimes recklessly. This is why they don't want to go to bed and will fight and cry to keep from doing so. Imagine an on-off switch in their minds that monitors time. When they are busy, i.e., having fun, the switch is off. When they are bored, it's on. Sitting still, or laying still in bed awaiting sleep to overtake them is boring because the time monitor switch is on, and the only activity they perceive is the passage of time. They don't understand this, of course, and really don't even understand the concept of time until close to 5 years old, but instinctively they understand what fun is.
As children grow older, they learn better to entertain themselves. They build their toolbox of activities they enjoy and their library of options to turn off the time monitor switch grows. As they move into their teen years and older, they continually replace some of their older tools with newer ones, and socialization with friends takes up some of their toolbox space. They are more aware of time, and are constantly bombarded by it as deadlines, responsibilities, commitments and schedules take over portions of their lives.
Life eventually becomes more and more about time, how to get more free time to do the "want to do stuff" and make the "have to do stuff" go away faster. People naturally procrastinate the "have to do stuff", which focuses them on time, keeping the time monitor switch in constant operation. But there is always more "want to do stuff" than can be squeezed into the available opportunities, so workweeks often seem to take forever, while weekends pass in a flash.
People eventually reach the age when their perspective changes from one of wanting to stay up late to get more done or experience more, to enjoying going to bed early because that time laying in bed awaiting sleep to overtake them is time they enjoy, and they don't get enough of it.
When people are older, they don't get bored as easily. Idle time becomes relaxation or reflection time and, when not relaxing or reflecting, they have a whole lifetime of building up those tools, so there is always something else enjoyable to do. The passage of time is always there, but it's in the background as something that has to be beaten before it comes to an end. To beat it, all a person needs to do is accomplish something, for example, "I want to visit Rome before I die" or "I want to finish building this piece of furniture". Success usually necessitates a flurry of activity, all of which keeps the time monitor switch off and makes time seem to pass more quickly.
There's a story in Bill Bennett's 'Children's Book of Virtue'; I can't recall the name of it; but it's about a person who desperately wants unpleasant time to pass quickly. Somehow he gets a ball of string and is told that to make time pass, all he has to do is let out a little string to move forward in time. He's cautioned that when the ball of string is gone, it will be the end of his life.
Throughout the story, each time he faces a difficult or unpleasant time, he pulls out a bit more string until eventually he reaches the end of his life. Only then does he realize how much of his life he wished away by pulling the string, and how many events, however unpleasant, he never experienced because of his impatience. He missed big events in his children's lives, as well as opportunities to say goodbye to loved ones before they passed away. While he was focused on avoiding a difficult time with a new boss, his children grew up and graduated. While he tried to avoid his own illness, he lost a parent. He is eventually given another chance at life, but in reality, we don't get second chances.
The moral of the story is to relish all the time we have, to make the most of it and not wish it away. It may seem to move slowly, or it may seem to pass in a flash, but either way it's all the time we have.