What an interesting thread and discussion.
When I go back to the original post, I see a problem statement that asks us to consider deceleration between two aircraft of different mass. (I assume the frame of reference is Earth, where a difference in weight can be equated to a difference in mass).
One is asked to explain the time it takes to change velocity from one value to another, with the only difference in initial condition being difference in mass. (Note that I had to make a number of assumptions to parse that problem statement).
I have enjoyed the seven pages of discussion into the esoterica of deceleration, rates, inertia, momentum, and enery in an aerodynamic context. Good stuff!
From the discussion, I find myself aligned with those people who approach the problem from the change in energy state. Were I asked that question with no help from 20 pound brains, that is the direction from which I would answer it.
Question asked:
Pardon me but..
1)Why do heavier aircrafts {sic} take longer to slow down in the air compared to lighter aircrafts? {sic}
This appears to me to be an example of begging the question, and indeed, assuming the answer to a question in the asking.
A more correctly phrased question would be:
Do heavier aircraft take longer to slow down in the air compared to lighter aircrafts? {sic} If so, why is that?
[QUOTE] 2)Why on high profile, it's recommended to increase speed? [QUOTE]
Is it? By whom?
Depending on how you are flying, you may wish to maintain approach speed and reduce power to increase rate of descent, or you may wish to increase drag by doing things like adjusting flaps, or dropping the landing gear to increase drag. (Or, if in a glider, descending in a slip to also increase drag ... )
Once again, I'd say we have an example of begging the question.
Provisional answer:
1) Given all other things being equal (which some of the above conversation suggests they might not be) and
assuming the "I need to slow down" action taken will be identical
in terms of what change to the aircraft is executed to change energy state (example, change a flap setting or reduce engine power an identical amount)
then the aircraft with the greater energy at the beginning would more likely take longer to slow down ... On The Assumption that they are both attempting to get to the same "V" when slowing down in the first place. (Can we assume that? )
I have been cheered to learn that "it's more complicated than that" during the discussion, because of aerodynamic unique considerations. Again, my thanks to the 20 pound brains.
I am not certain the person framing the question was clear on that or not.
2) The permutations of what to do with your energy state to change profile if you are high were not, in my training, generally to speed up to change profile errors, unless one were ALSO slow and while being high on profile.
The problem statement omits what actual initial conditions are, which leaves us guessing. I'd answer question number two differently:
If you are high on profile and slow, then speeding up is a part of returning to profile.
If not, then speeding up may not be the best way to resolve your being off of profile to begin with.
For example, if you have time to change configuration early, perhaps you dive, speed up, and then dirty up early so as not to get to close to the plane ahead of you ... there's a lot to this answer left open in the question.
To answer number two, on basic principles, I'd allude to "Power plus attitude (for a given cofiguration) equals performance" in powered flight.
This answer is not provided by an aero engineer, it was provided by a pilot. Sure, I have a degree in mechanical engineering, but I can't hang with the 20 pound brains in this thread. (You all know who you are!
Goodonya, all of you!)
Talking about gliders seems a red herring in this discussion.