It speeds up for two reasons.

The first reason is that each increment of subjective time that passes is constant, but its perception is like an expression in calculus, dt/t. dt is that moment in time, infinitely small, or an hour, or a day, or a year, or whatever. Whatever dt is, the quantity dt/t is how you perceive it. As t increases (as you get older), the quantity gets smaller, and you barely feel time slipping by at all. Forget all the silly math analogies, I'm just saying that a minute is longer for a child because their shorter lives are all they have to compare it to, and, as such, that minute will take longer.

The next reason is more depressing. When you're a child, each moment is a miracle. Life is full of puzzles and learning experiences. This continues as you go through school and grow up, puberty whizzes by, you meet the opposite sex, but after awhile things just lag. There aren't too many new experiences. You get up, go to work, have dinner, watch some TV show, and go to bed and repeat. On the weekends you do fun things, but it isn't long before everything seems the same. Without any miracles, each day becomes a brown blur. Pretty soon, you're on your death bed.

Death becomes the integral of dt/t, and what does it equal? The answer's only natural, I guess.

Umm ... I can't exactly provide a clear answer for you, since I am not old enough and don't have that experience. :(

However, I suppose older people may feel the time is speeding up because most of the time, they are used to sit in one place and concentrate on one subject. Younger people mostly are mobile and quick, they do not feel much about the time. (I sometimes, have wondered how much time has been gone when I am sitting in my class listening to my teacher)

Also when people become of old age, their movements start to slow up, and therefore, they take a lot of time to finish up their works. That may also be a reason for them to feel time is speeding up. Life is full of adventures when you are younger, and when you become older, the life turns into a definite routine and leading to boredom. That may also be a reason for feeling boredom.

Hope this helps !

I call it Einstein's pseudo-theory of relativity. As you get older each moment you live becomes an ever-shrinking fraction of your whole life up to that point. When you're ten, a year is a whole tenth of your life. When you're 70, a year is one seventieth of your life. Even though the year has not changed in length your perspective of it has. When you're 20, ten years is a whole half of your life. When your 60, ten years is the same as ten minute is to an hour, ten seconds is to a minute.