Final answer:
The slope of the position vs. time graph represents velocity, while the slope of the velocity vs. time graph represents acceleration. Instantaneous velocity is the slope of the tangent line at a particular point on the position vs. time graph.
Step-by-step explanation:
The slope of the position vs. time graph represents the object's velocity. If we have a straight line with a positive slope on such a graph, the object is moving at a constant velocity; the steeper the slope, the faster the object is moving. Conversely, if the slope is decreasing and approaching zero, the object's velocity is also decreasing. Instantaneous velocity can be determined by drawing a tangent to the curve at a specific point and calculating the slope of this tangent line, which is done by dividing the rise (change in position) by the run (change in time).
When examining the slope of a velocity vs. time graph, we are looking at the object's acceleration. In this case, slope is calculated as the change in velocity over the change in time. Therefore, a positive y-intercept on a velocity vs. time graph indicates initial velocity and a negative slope indicates that the object is decelerating.