What is the difference between a position time graph and a velocity time graph?

Answer 1

The velocity-time graph plots the DERIVATIVE of the position-time graph, as a function of time. In other words, this velocity-time graph actually shows you the history versus time of the SLOPE of the position-time graph. Conversely, the position-time graph shows you the INTEGRAL of the velocity-time graph with respect to TIME.

The height of the points in the latter graph, however, is uncertain by an arbitrary constant. What that means is that although the VELOCITY HISTORY of two problems may have been identical, in one of them you may have been making your POSITION measurements from any arbitrary place --- that is, in a second example, from MILES AWAY from where the object actually started in the first example, while all the time exhibiting EXACTLY the SAME velocity. So: if what you're given as primary data is the velocity-time graph, with NO information about position at some given time, the absolute height of your position-time points is uncertain to within a constant. The other way round, there's NO uncertainty involved: the slope of the position-time graph at any given time is INDEPENDENT of whether you add an ARBITRART CONSTANT to the measurements of ALL positions as a function of time.

Live long and prosper.

Answer 2

velocity is the derivative of the the position function with respect to time.
The position time graph would plot distance versus time.
The velocity time graph would plot the speed versus time.

a Velocity time graph which is a horizontal line above the axes, would equate to a position time graph that is a straight line starting low at early times and high at later time.

Answer 3

Because the velocity time graph is the derivative of the position time graph, it will represent the slope of the line.

Answer 4

Position time graph shows you the velocity. (rate of change of position with respect to time)
Velocity time graph shows you the acceleration (rate of change of velocity with respect to time)