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## Introduction

Velocity is a fundamental concept in physics that describes the rate of change of an object’s position with respect to time. It is a vector quantity, meaning it has both magnitude and direction. Velocity is a key parameter for understanding the motion of objects and plays a significant role in various scientific and everyday applications.

Unlike speed, which solely indicates the magnitude of motion regardless of direction, velocity distinguishes itself by providing both the speed and direction of an object’s motion. While speed informs us about the object’s rate of movement, velocity goes further by specifying the speed and direction in which the object is moving. For example, if a car is traveling at a constant speed of 60 kilometers per hour, its velocity would be 60 kilometers per hour in a specific direction, such as east or west.

## Velocity Definition

Velocity is defined as the displacement (change in position) of an object divided by the time taken for that displacement.

### Velocity Formula

The formula for calculating average velocity is:

**Avg. Velocity = Displacement/Time**

The displacement (Δx) signifies the alteration in an object’s position, measured in a specific direction, whereas the time (Δt) corresponds to the duration over which the displacement took place. Average velocity furnishes insights into the overall positional change within a designated time frame.

Instantaneous velocity denotes the velocity of an object at an exact moment in time. It is determined by computing the limit of the average velocity as the time interval approaches zero. Instantaneous velocity precisely captures the velocity of an object at any given instant.

### Positive Vs Negative Velocity

Velocity can be positive, negative, or zero, depending on the direction of motion. A positive velocity indicates motion in the positive direction, while a negative velocity represents motion in the opposite direction. Zero velocity signifies that the object is not changing its position.

Velocity is closely related to the concept of acceleration. Acceleration measures the rate of change of an object’s velocity with respect to time. If an object’s velocity changes, it means the object is experiencing acceleration. Acceleration can be positive (speeding up) or negative (slowing down), and it affects the object’s velocity accordingly.

### Unit of Velocity

The established SI unit for Velocity is the same as that of speed. That is meters per second. However, velocity can also be expressed in other units depending on the context, such as kilometres per hour (km/h), miles per hour (mph), or feet per second (ft/s).

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### Solved examples on Velocity Formula

**Example 1: A car travels a distance of 200 kilometres in 4 hours. Calculate its average velocity.**

**Solution:** Given,

Distance (d) = 200 km

Time (t) = 4 hours

To calculate average velocity, we use the formula:

Average Velocity (v) = Displacement (Δx) / Time (Δt)

In this case, since the car travelled a straight distance without any change in direction, the displacement is equal to the distance covered. So, the displacement (Δx) is 200 km.

Substituting the values into the formula:

v = 200 km / 4 hours

v = 50 km/h

Therefore, the average velocity of the car is 50 kilometres per hour.

**Example 2: Imagine a scenario where a car driver completes a 300 km race within a time span of one hour and forty minutes on a racetrack where the start line and the finish line coincide. What was the average velocity of that car?**

**Solution:** The driver started the race and ended it at the same point. This means the displacement of the car is zero. And zero divided by the taken time, which is one hour forty minutes equals zero. That puts the average velocity for the race today at zero meters per second.

**Example 3: A train travels a distance of 500 meters in 25 seconds. Calculate its velocity.**

**Solution:** Given,

Distance (d) = 500 meters

Time (t) = 25 seconds

To calculate velocity, we use the formula:

Velocity (v) = Distance (d) / Time (t)

Substituting the given values into the formula:

v = 500 meters / 25 seconds

v = 20 meters per second

Therefore, the velocity of the train is 20 meters per second.

## Frequently Asked Questions on Velocity Formula

### What is velocity?

Velocity is a vector quantity that represents the rate of change of an object's position with respect to time. It includes both the speed and direction of motion.

### How is velocity different from speed?

While both velocity and speed describe how fast an object is moving, velocity also specifies the direction of motion, whereas speed does not consider direction.

### What is the SI unit of velocity?

The SI unit of velocity is meters per second (m/s).

### Is velocity a scalar or a vector?

Velocity is a vector quantity. It not only represents the magnitude of speed but also includes direction. As a vector, velocity has both magnitude (speed) and direction, which allows us to describe both how fast an object is moving and the direction it is moving in. The vector nature of velocity enables us to differentiate between objects moving at the same speed but in different directions.

### What is the rate of speed?

The term rate of speed is not commonly used in physics. However, if referring to the rate at which speed changes, it is referred to as acceleration. Acceleration measures the change in velocity per unit of time, indicating how quickly an object's speed is increasing or decreasing.

### What are the types of velocity?

Velocity can be categorized into two main types- Average Velocity, Instantaneous Velocity.

### How is average velocity calculated?

Average velocity is determined by dividing the displacement of an object by the time taken. The formula is: Average Velocity = Displacement / Time.

### What is the difference between average velocity and instantaneous velocity?

Average velocity represents the overall change in position over a given time interval, while instantaneous velocity refers to the velocity of an object at a specific instant in time.

### Can velocity be negative?

Yes, velocity can be positive, negative, or zero. A positive velocity indicates motion in one direction, a negative velocity represents motion in the opposite direction, and zero velocity means no motion.