Whenever a moving object changes its speed, we say that its motion is non-uniform.

In this lesson, learn more about non-uniform motion and how to analyze it graphically.

## What Is Uniform Motion?

Imagine that you could take a picture of a car traveling down a straight road every second. It might look something like the diagram that you’re seeing on your screen right now.

Did you notice that the car travels the exact same distance every second? That’s because this is an example of **uniform motion**, in which an object travels equal distances in equal time intervals.

If any object has uniform motion, then it also has a constant velocity.One way to represent the motion of an object is to make a position-time graph. If you made a graph of the car’s position over the three seconds shown, it would look like the one on your screen right now.

Looking at this graph, you can tell right away that the motion is uniform, because the graph forms a straight line with a constant slope. The slope of a position-time graph will tell you the velocity of an object, which is 10 m/s for the car shown earlier.

## What Is Non-Uniform Motion?

We’ve seen what uniform motion looks like, but objects don’t always exhibit uniform motion.

Many times, they speed up or slow down so that their motion is no longer uniform. Let’s look at the car again, and see what’s happening now.

Does it still have uniform motion? No, you can see that now the car is going a different distance in each second.

When objects like this car exhibit **non-uniform motion**, it means that they travel different distances in equal time intervals. In this case, during the first second the car travels 5 m. It travels 10 m during the next second, and then 15 m during the third second.What would this look like on a position-time graph? Let’s plot these points and see:

Unlike the graph of uniform motion, this position-time graph of non-uniform motion does NOT have a constant slope, because the velocity of the car is changing every second. In the first second, the velocity is only 5 m/s, but this increases to 15 m/s by the third second.

When the velocity of a moving object changes, then it has an acceleration. **Acceleration** is defined as the rate of change of an object’s velocity. To calculate acceleration graphically, we need a new type of graph. If you graph the object’s velocity vs. time, the slope of the resulting velocity time graph will tell you how quickly the velocity of the object is changing, which is its acceleration.We have already calculated the velocity of the car during each of the three seconds. Now let’s plot these points on a velocity time graph, and use it to calculate the acceleration of the car.

You may have noticed that the points we used for time were 0.5 s, 1.5 s, and 2.5 s.

Why didn’t we just use 1, 2, and 3 seconds like we did on the position-time graph? To understand this, look at the position-time graph again. We calculated the average velocity of the car during the first second to be 5 m/s. Since this is an average from 0 – 1 second, it makes sense to plot this velocity at the point that’s right in the middle between 0 and 1 seconds, which is 0.5 s.

The same applies for the other two points shown on the graph.From this graph, we can determine that the acceleration of the object is 5 m/s2. This means that for every second the car is moving, it increases its velocity by 5 m/s.

## Lesson Summary

**Uniform motion** occurs when an object travels equal distances in equal time intervals.

Uniform motion happens when the object is moving with a constant velocity.**Non-uniform motion** occurs when an object travels different distances in equal time intervals. This happens when the object is speeding up or slowing down, so its velocity is changing.You can determine if an object exhibits uniform motion by looking at a position-time graph of the motion. If the graph forms a straight line with a constant slope, then the motion is uniform, and the slope of the graph is equal to the velocity of the object.

If an object exhibits non-uniform motion, a position-time graph of the motion will be curved, not straight. If you graph the velocity of the object vs. time, then this graph will tell you how quickly the velocity is changing, a quantity called **acceleration**.

The slope of a velocity-time graph gives you the acceleration of the object.