In physics, uniform motion refers to the motion of an object when it covers equal distances in equal intervals of time. This means that the object moves at a constant or fixed speed throughout its journey. The distance covered by the object increases directly with time.

Mathematically, uniform motion can be described using the following equation:

```

Speed = Distance covered / Time taken

```

where:

- Speed is the rate at which the object is moving, expressed in units such as meters per second (m/s) or kilometers per hour (km/h)

- Distance covered is the total distance traveled by the object in a given time, expressed in units such as meters (m) or kilometers (km)

- Time taken is the duration of the object's motion, expressed in units such as seconds (s) or hours (h)

For uniform motion, the speed remains constant throughout. Therefore, if you plot a graph of the object's displacement or distance covered on the y-axis against time on the x-axis, you will obtain a straight line with a constant slope.

Here are some real-world examples of uniform motion:

1. A car moving on a straight highway at a steady speed of 60 km/h.

2. A runner covering a certain distance on a track in equal time intervals.

3. A bicycle moving down a slope with a constant velocity.

In contrast to uniform motion, non-uniform motion is when an object's speed or velocity changes during its motion. This results in a curved path or an acceleration of the object. Examples of non-uniform motion include a car speeding up or slowing down, or a ball thrown into the air.