Speed and velocity are fundamental concepts in physics that describe the motion of an object. While they are related, they have distinct meanings and implications. Here are the key differences between speed and velocity:

### Definition

- **Speed**:

- A scalar quantity that refers to how fast an object is moving.

- It is the rate at which an object covers distance.

- Speed is given by the formula: \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)

- **Velocity**:

- A vector quantity that refers to the rate at which an object changes its position.

- It includes both the speed and direction of the object's motion.

- Velocity is given by the formula: \( \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} \)

### Nature

- **Speed**:

- Scalar quantity: Only has magnitude (how fast).

- Does not include direction.

- Example: 50 km/h.

- **Velocity**:

- Vector quantity: Has both magnitude and direction.

- Includes the direction of motion.

- Example: 50 km/h east.

### Calculation

- **Speed**:

- Calculated as the total distance traveled divided by the total time taken.

- Speed = \( \frac{\text{Total Distance}}{\text{Total Time}} \)

- Example: If a car travels 100 km in 2 hours, its speed is 50 km/h.

- **Velocity**:

- Calculated as the total displacement divided by the total time taken.

- Displacement is the straight-line distance from the starting point to the endpoint.

- Velocity = \( \frac{\text{Total Displacement}}{\text{Total Time}} \)

- Example: If a car travels 100 km east in 2 hours, its velocity is 50 km/h east.

### Direction

- **Speed**:

- Does not involve direction.

- Only indicates how fast an object is moving.

- **Velocity**:

- Involves direction.

- Indicates how fast and in which direction an object is moving.

### Constancy

- **Speed**:

- Can remain constant even if the object changes direction.

- Example: A car moving in a circular track at a constant speed of 60 km/h.

- **Velocity**:

- Changes if either the speed or the direction changes.

- Example: A car moving in a circular track at a constant speed has a constantly changing velocity due to the change in direction.

### Average and Instantaneous

- **Speed**:

- **Average Speed**: Total distance traveled divided by the total time taken.

- **Instantaneous Speed**: The speed of an object at a specific moment in time.

- **Velocity**:

- **Average Velocity**: Total displacement divided by the total time taken.

- **Instantaneous Velocity**: The velocity of an object at a specific moment in time.

### Examples

- **Speed**:

- If you drive 150 km in 3 hours, your average speed is 50 km/h.

- If a runner completes a 400-meter lap in 1 minute, the speed is 400 meters per minute.

- **Velocity**:

- If you drive 150 km east in 3 hours, your average velocity is 50 km/h east.

- If a plane flies 600 km north in 2 hours, its velocity is 300 km/h north.

### Summary

- **Speed**:

- Scalar quantity: magnitude only.

- Formula: \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)

- Example: 60 km/h.

- **Velocity**:

- Vector quantity: magnitude and direction.

- Formula: \( \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} \)

- Example: 60 km/h north.

Understanding these differences is crucial in physics and various real-world applications, such as navigation, engineering, and motion analysis.