Table of Contents

Average velocity is a measure of the overall rate of change in the position of an object over a specific time interval. It is calculated by dividing the change in displacement by the change in time. The formula for average velocity can be expressed as:

**Average velocity = (Displacement change) / (Time change) **

Mathematically, it can be represented as:

Average velocity = (x_{f} – x_{i}) / (t_{f} – t_{i})

Where “x_{f}” represents the final position, “xi” represents the initial position, “t_{f}” represents the final time, and “t_{i}” represents the initial time.

It’s important to note that average velocity is a vector quantity, which means it has both magnitude and direction. The displacement change in the numerator takes into account the object’s change in position, while the time change in the denominator reflects the duration of that change.

## To calculate the average velocity, follow these steps

- Determine the final position (x
_{f}) and initial position (x_{i}) of the object along the chosen direction. For example, if an object moves along a straight line, the positions could be represented by numerical values or coordinates. - Determine the final time (t
_{f}) and initial time (t_{i}) corresponding to the time interval during which the object undergoes the displacement. - Subtract the initial position from the final position to obtain the displacement change (x
_{f}– x_{i}). - Subtract the initial time from the final time to obtain the time change (t
_{f}– t_{i}). - Divide the displacement change by the time change to calculate the average velocity.

The average velocity formula is widely used in various fields, including physics, engineering, and sports. It helps in analyzing and describing the motion of objects, calculating rates of change, and making predictions about future positions. It is important to note that average velocity represents the overall behavior of an object over a given time interval and may not capture any instantaneous changes in velocity that might occur during that interval.

### Solved Examples on Average Velocity Formula

**Example 1**: A person walks 2 kilometers east and then 1 kilometer west in a total of 1 hour. What is their average velocity?

**Solution: **

Given:

Displacement (change in position) = 2 km east – 1 km west = 1 km east

Time is taken (change in time) = 1 hour

Using the average velocity formula:

Average velocity = Displacement / Time taken

Average velocity = 1 km / 1 h

Average velocity = 1 km/h east

Therefore, the person’s average velocity is 1 kilometer per hour east.

**Example 2: **A car starts from rest and accelerates uniformly at a rate of 2 m/s² for a time interval of 10 seconds. What is the average velocity of the car during this time?

**Solution: **

Given:

Acceleration (a) = 2 m/s²

Time (t) = 10 seconds

To find the average velocity, we need to determine the displacement of the car during the given time interval.

Using the kinematic equation:

v = u + at

Where:

v is the final velocity,

u is the initial velocity (which is 0 m/s since the car starts from rest),

a is the acceleration, and

t is the time.

Calculating the final velocity:

v = u + at

v = 0 + (2 m/s²)(10 s)

v = 20 m/s

The final velocity of the car after 10 seconds of uniform acceleration is 20 m/s.

Now, we can calculate the displacement of the car using another kinematic equation:

s = ut + (1/2)at²

Where:

s is the displacement.

Since the initial velocity (u) is 0 m/s, the equation simplifies to:

s = (1/2)at²

s = (1/2)(2 m/s²)(10 s)²

s = (1/2)(2 m/s²)(100 s²)

s = 100 m

The displacement of the car during the 10-second interval is 100 meters.

Finally, we can calculate the average velocity:

Average velocity = Displacement / Time taken

Average velocity = 100 m / 10 s

Average velocity = 10 m/s

Therefore, the average velocity of the car during the 10-second time interval is 10 meters per second.

## Frequently Asked Questions on Average Velocity Formula

### How is average velocity different from average speed?

Average velocity and average speed are related but different. Average velocity considers both the magnitude and direction of an object's displacement, while average speed only considers the magnitude of the total distance travelled divided by the total time taken, without regard to direction.

### How is average velocity calculated?

Average velocity is calculated by dividing the change in displacement by the change in time. Mathematically, it can be expressed as: Average velocity = (Displacement change) / (Time change).

### Is average velocity a scalar or a vector quantity?

Average velocity is a vector quantity as it has both magnitude (speed) and direction. The direction of the average velocity represents the direction of the displacement.

### Can average velocity be zero even if an object is in motion?

Yes, it is possible for the average velocity to be zero even if an object is in motion. This occurs when an object moves back and forth, covering equal displacements in opposite directions over a given time interval.

### How is average velocity represented graphically?

Average velocity can be represented graphically as the slope of a position vs. time graph. The slope is calculated by dividing the change in displacement by the change in time.

### How does average velocity relate to instantaneous velocity?

Average velocity represents the overall behavior of an object over a time interval, while instantaneous velocity refers to the velocity of an object at a specific moment in time. Instantaneous velocity can be found by calculating the derivative of the displacement with respect to time.

### What are the units of average velocity?

The units of average velocity depend on the units used for displacement and time. Common units include meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph).