Question

Name the physical quantity measured by the velocity-time graph?

Answer 1

The so-called "velocity-time" graph is actually a "speed-time" graph.  At any point
on it, the 'x'-coordinate is a time, and the 'y'-coordinate is the speed at that time.

'Velocity' is a speed AND a direction.  Without a direction, you do not have a velocity,
and these graphs never show the direction of the motion.  It seems to me that it would be
pretty tough to draw a graph that shows the direction of motion at every instant of time,
so my take is that you'll never see a true "velocity-time" graph. 

At best, it would need a second line on it, whose 'y'-coordinate referred to a second
axis, calibrated in angle and representing the 'bearing' or 'heading' of the motion at
each instant. The graph of uniform circular motion, for example, would have a straight
horizontal line for speed, and a 'sawtooth' wave for direction.