Final answer:
The slope at a point on a position versus time graph represents the object's instantaneous velocity. A line tangent to the curve at that point gives the velocity, and a velocity versus time graph's slope would represent acceleration.
Step-by-step explanation:
The slope at a point on a position versus time graph of an object is instantaneous velocity. To determine the instantaneous velocity at any specific point, one draws a straight line tangent to the curve at that point, and calculates the slope of that tangent line. The slope is defined as rise over run, meaning the change in position (vertical axis) divided by the change in time (horizontal axis). As the velocity of an object changes, this is reflected in the steepness of the slope on the position versus time graph; steeper slopes indicate higher velocities.
Furthermore, if you create a velocity versus time graph by plotting the instantaneous velocities over time, the slope of this new graph represents acceleration, which is the change in velocity over the change in time. Therefore, by analyzing the relationship between position, velocity, and acceleration through their respective slopes on a graph, one can gain a comprehensive understanding of an object's motion.