Part of the science of physics is the measurement of the motion of objects. 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 said to be derived from the position-time graph. Similarly, the acceleration-time graph is said to be derived from the velocity-time graph. The various graphical representations of motion are related through the slopes of each graph.
The Position-Time Graph
The position-time graph is used in physics to describe 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, measured 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. If the slope of a position-time graph is constant, this indicates a velocity that is constant. A position-time graph with a varying slope indicates a changing velocity. The direction of the slope of the position-time graph indicates the sign of the velocity. For example, if the slope of a position-time graph 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 velocity-time graph that is a straight line. 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, then 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, then the acceleration is increasing. If slope is negative, acceleration is decreasing.