# Kinematics: Definition & Graphical Representation

Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After completing this lesson, you will be able to explain what kinematics is, and how graphical representations are used in kinematics. A short quiz will follow.

## What Is Kinematics?

Kinematics is the study of motion, without any reference to the forces that cause the motion. It basically means studying how things are moving, not why they're moving. It includes concepts such as distance or displacement, speed or velocity, and acceleration, and it looks at how those values vary over time.

Kinematics can be studied in one dimension, like a bus driving along a straight road; in two dimensions, like a canon being fired with a side-on view; and even in three dimensions. Things just get a little more complicated as you add dimensions.

Kinematics has many equations associated with it: equations for objects moving at a constant speed, equations for objects that are accelerating, even complex equations for objects where the acceleration rate is changing. But sometimes it's easier to use graphical representations of kinematics quantities or, in a word, graphs.

## Motion Graphs

There are three main motion graphs that tend to be studied in kinematics: displacement-time graphs, velocity-time graphs, and acceleration-time graphs. Displacement is a lot like distance - to be exact, it's how far you are from your starting position. Velocity is like speed, but with a direction. For example, 5 miles per hour is a speed, 5 miles per hour north is a velocity. And acceleration is the rate at which the velocity is changing.

Here is an example of a displacement-time graph:

It shows an object moving at a constant speed away from its starting position, and then slowing down to a stop.

To plot a velocity-time graph of this motion, we can either think conceptually about what's happening, or find the slope of the displacement-time graph. The slope of the displacement-time graph tells you the velocity. A velocity-time graph of the same motion looks like this:

We see a constant velocity at first, and then the object slows down to a stop. Or in other words, we have a positive velocity where the slope of the displacement graph was positive, and a velocity decreasing to zero where the slope of the displacement graph was flattening off to zero.

Now, to move on to an acceleration-time graph we can do the same thing again - think about how the velocity is changing conceptually, or find the slope of the velocity-time graph. The slope of the velocity-time graph tells you the acceleration. And an acceleration-time graph of the same motion looks like this:

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