why don't the glasses of water fall when we pull the table cloth quickly enough?

Answer 1

Both above are correct.

When you pull the tablecloth out from under the glass, there is a certain amount of friction that may start to accelerate the glass. The glass isn't "motionless" but once the tablecloth is out from under it, the friction with the table slows whatever glass velocity that was established.

If you pull slowly, the friction doesn't change but the lower required acceleration doesn't make the force of acceleration high enough to be a "breakaway" force. (put a block on a board and slowly tip the board. when the block "lets go" and slides the force to hold it to the board is not sufficient.)

High jerk (also known as rate of change of acceleration) of the tablecloth gets it all done before the glass can accelerate (0 velocity due to its relative inertia).

Low jerk makes you look like a jerk because all the glasses hit the floor and most likely break.

Answer 2

Low friction against the table cloth.
Gravity acting on the glass.
Have a nice day.

Answer 3

Because there is a difference between 'efficient friction' (more friction) and 'coefficient friction' (less friction).
If you pull the cloth slowly, you have 'efficient friction' between the cloth and the glass.
If you pull the cloth fast, you have 'coefficient friction' between the cloth and the glass.

Answer 4

Newton's Law: Objects at rest tend to stay at rest and objects in motion tend to stay in motion.