Motion with Position vs. Time Graphs – Mechanical Engineering

# The Meaning of Shape for a p-t Graph

Our study of 1-dimensional kinematics has been concerned with the multiple means by which the motion of objects can be represented. Such means include the use of words, the use of diagrams, the use of numbers, the use of equations, and the use of graphs. Lesson 3 focuses on the use of position vs. time graphs to describe motion. As we will learn, the specific features of the motion of objects are demonstrated by the shape and the slope of the lines on a position vs. time graph. The first part of this lesson involves a study of the relationship between the shape of a p-t graph and the motion of the object.

### Contrasting a Constant and a Changing Velocity

To begin, consider a car moving with a constant, rightward (+) velocity – say of +10 m/s.

If the position-time data for such a car were graphed, then the resulting graph would look like the graph at the right. Note that a motion described as a constant, positive velocity results in a line of constant and positive slope when plotted as a position-time graph.

Now consider a car moving with a rightward (+), changing velocity – that is, a car that is moving rightward but speeding up or accelerating.

If the position-time data for such a car were graphed, then the resulting graph would look like the graph at the right. Note that a motion described as a changing, positive velocity results in a line of changing and positive slope when plotted as a position-time graph.

The position vs. time graphs for the two types of motion – constant velocity and changing velocity (acceleration) – are depicted as follows.