Re: What is the physical significance of 'square of velocity' or '/sec square'?

Greetings, Himanshu:

While it is not erroneous to seek to better understand Physics,
it can be erroneous to look for things that aren't necessarily
there.  For example, consider an item from Advanced Physics
known as the "fine structure constant".  This is a pure number,
approximately 1/137 -- it has no accompanying measurement-units
of any sort!  Like the number pi (3.14159...), it is a ratio
associated with certain measured things -- but pure numbers,
WHEN TAKEN OUT OF CONTEXT, have no physical significance
whatsoever.

Similarly, the square of a velocity, or the reciprocal of the
square of a time-duration, cannot with certainty be said to
have physical meaning in and of themselves -- they have been
taken out of context.

Naturally, that means that within the appropriate context, those
portions of complete expressions do contribute to some overall
physical meaning.  When a squared velocity is multiplied by some
amount of mass, we find that the WHOLE expression is the
description of Energy.  And when the reciprocal of a squared
time-duration is multiplied by some amount of distance, we find
that the WHOLE expression describes Acceleration.

Well, I hope you won't have found this Answer too disappointing.
As for the fine structure constant, what is its context?  To the
best of my knowledge, there is a minor mystery here.  It's a
number that 'just happens' to appear when certain physical
quantities, like the speed of light and the strength of the
electric charge on the electron (or proton), are assembled
into a particular mathematical expression.  It may be nothing
more than a curiosity, that all those physical units of
measurement can manage to completely cancel each other out in
that particular expression, leaving an oddball number behind.
Or it may actually mean something important, that has not yet
been identified with certainty.  One possibility that has been
suggested relates to the ratio of strengths of the
Electromagnetic and Strong Nuclear Forces.  The former is
certainly more than 114 times weaker than the latter, because
we CAN assemble that many protons together into a single atomic
nucleus, despite their combined mutual electric repulsion.
Whether or not the actual ratio is about 1:137 remains to be
determined.