Speed:
Speed is a scalar quantity that refers to "how fast an object is moving." It is a measure of the distance covered per unit of time, without considering the direction of motion. The formula to calculate speed is given by:

Speed = Distance / Time

Speed can be measured in various units such as meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph).

Velocity:
Velocity is a vector quantity that includes both speed and direction. It not only considers "how fast an object is moving" but also "in which direction it is moving." The formula to calculate velocity is given by:

Velocity = Displacement / Time

Velocity is also measured in units such as meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph).

Difference between Speed and Velocity:

1. Definition:
- Speed: It refers to how fast an object is moving, without considering the direction.
- Velocity: It refers to how fast an object is moving and in which direction it is moving.

2. Scalar vs. Vector:
- Speed: It is a scalar quantity as it only has magnitude.
- Velocity: It is a vector quantity as it has both magnitude and direction.

3. Consideration of Direction:
- Speed: It does not consider the direction of motion.
- Velocity: It considers the direction of motion.

4. Representation:
- Speed: It is represented by a single numerical value followed by the unit.
- Velocity: It is represented by a numerical value followed by the unit and a direction (e.g., 30 m/s east).

5. Change with Direction:
- Speed: It remains the same regardless of the direction of motion.
- Velocity: It can change even if the speed remains the same, as long as the direction changes.

6. Example:
- Speed: An object traveling at 60 km/h has a speed of 60 km/h.
- Velocity: An object traveling at 60 km/h north has a velocity of 60 km/h north.

7. Importance:
- Speed: It is important in determining how fast an object can cover a distance.
- Velocity: It is important in determining the displacement of an object and its direction.

In conclusion, speed and velocity are related but distinct concepts. While speed only considers the magnitude of motion, velocity takes into account both the magnitude and direction of motion. It is crucial to understand the difference between these terms to accurately describe and analyze the motion of objects.

Speed is distance travelled per unit time whereas velocity is distance travelled per unit time in a given direction.