What is the difference between a distance vs. time graph and a position vs. time graph?
When measuring an object's motion, it is usually the case to measure quantities as a function of time. That is, time is the independent variable.
The simplest quantityto consider is the object's position as it changes with time. To do this analysis one would record the time in regular intervals and the amount of distance the object has moved as measured from the origin over each interval. This data can the plotted on a Cartesian (x,y) coordinate axis with the horizontal axis being the time and the associated displacement being the vertical axis. The result in graph would be a distance vs. time graph.
You could then analyze this graph and draw some conclusions about the motion. If the data forms a straight line we can conclude that the object is moving with a constant speed. If the slope is positive (up as you go from left to right), it has a positive constant velocity; if slope is negative, the velocity is negative. If the slope is zero (horizontal line), then the object is not moving.
If the data points do not form a straight line, but a curve instead, we can conclude that the object is not traveling at a constant speed: it is accelerating or decelerating.