Define the distance an object travels per unit of time and its relevance in kinematics.

Distance per unit of time is commonly referred to as speed in the context of kinematics, which is a branch of mechanics dealing with the motion of objects without considering the forces that cause the motion. Speed is a scalar quantity that measures how fast an object is moving. The relevance of speed in kinematics lies in its ability to describe the rate at which an object covers distance over time.

To define speed mathematically, we use the following formula:

$$
\text{Speed} = \frac{\text{Distance traveled}}{\text{Time taken}}
$$

Where:
- Speed is the distance an object travels per unit of time.
- Distance traveled is the total length of the path taken by the object.
- Time taken is the duration over which the motion occurs.

The standard SI unit for speed is meters per second (m/s), although other units like kilometers per hour (km/h) or miles per hour (mph) are also commonly used.

Let's go through a step-by-step solution to calculate the speed of an object given the distance traveled and the time taken.

Step 1: Identify the distance traveled and the time taken.
Suppose an object travels a distance of 150 meters over a period of 30 seconds.

Step 2: Write down the formula for speed.
$$
\text{Speed} = \frac{\text{Distance traveled}}{\text{Time taken}}
$$

Step 3: Plug the values into the formula.
$$
\text{Speed} = \frac{150 \text{ meters}}{30 \text{ seconds}}
$$

Step 4: Calculate the speed.
$$
\text{Speed} = \frac{150}{30} \text{ m/s} = 5 \text{ m/s}
$$

Step 5: Interpret the result.
The object's speed is 5 meters per second, which means that for every second of travel, the object covers a distance of 5 meters.

Understanding speed and its calculation is fundamental in kinematics as it allows us to predict where an object will be at a certain time, determine travel times, and compare the motions of different objects. It is also the basis for defining other kinematic quantities such as velocity (which includes direction) and acceleration (which is the rate of change of velocity).