A big part of the science of physics involves measuring the motion of objects, from a ball to a steam train. This includes plotting an object's position, velocity, acceleration and other relevant data. The graphical representation of one form of motion can lead to the graphs of the other forms of motion. For instance, the velocity-time graph is derived from the position-time graph. Similarly, the acceleration-time graph is derived from the velocity-time graph. The slopes of each graph relate to the various graphical representations of motion.
TL;DR (Too Long; Didn't Read)
The velocity-time graph is derived from the position-time graph. The difference between them is that the velocity-time graph reveals the speed of an object (and whether it is slowing down or speeding up), while the position-time graph describes the motion of an object over a period of time.
The Position-Time Graph
The position-time graph describes the motion of an object over a period of time. Time in seconds is conventionally plotted on the x-axis and the position of the object in meters is plotted along the y-axis. The slope of the position-time graph reveals important information about the velocity of the object.
Slope of the Position-Time Graph
The slope of a position-time graph reveals the type of velocity an object undergoes during its motion. A constant slope of a position-time graph indicates a constant velocity. A varying slope of a position-time graph indicates a changing velocity. The direction of the slope of the position-time graph indicates the sign of the velocity. For example, if it slopes downward, from left to right, the velocity is negative.
The Velocity-Time Graph
The velocity-time graph of an object reveals the speed at which an object is moving at a given time and whether it is slowing down or speeding up. Time in seconds is usually plotted on the x-axis while the velocity in meters per second is usually plotted along the y-axis. Objects moving at a constant rate have a straight-line velocity-time graph. Objects moving at variable speeds have sloping, linear velocity graphs.
Slope of the Velocity-Time Graph
The slope of the velocity-time graph reveals the acceleration of an object. If the slope of the velocity-time graph is a horizontal line, the acceleration is 0. This means the object is either at rest or moving at a constant speed, without speeding up or slowing down. If the slope is positive, the acceleration is increasing. If slope is negative, acceleration is decreasing.