# Average Velocity Study Guide

What is Average Velocity?

We generally hear that now everyone wishes to pitch a baseball as fast as they can. In fact, we all idealise the famous rookie Aroldis Chapman for his 105.1 miles per hour fireball. But the term ‘fast’ here is a vague term for the physical concept of velocity. The maximum speed of a specific pitch at any moment from its release to the time it crosses home plate is represented as **velocity**, one of the most commonly utilized tools for evaluating pitchers.

### Finding Average Velocity

Finding average velocity is similar to finding average speed, and it’s the rate at which an object moves over time.

## VELOCITY AND SPEED

The terms speed and velocity are commonly used interchangeably in everyday language to describe how **fast an object is moving**. Nevertheless, they are significantly different in physics. The magnitude of an object’s velocity, regardless of direction, is called **speed**. **Velocity** rather encompasses both speed and direction. Because it’s a vector, it needs a magnitude and a direction.

## AVERAGE VELOCITY

**Average velocity’s**definition is the time duration of the object selected divided by the displacement in relation to the initial position.- To put it another way, it’s the rate at which an object
**moves over time**. - The SI unit of average velocity is similar to the average speed, in
**meters per second**. - The average velocity’s direction is the displacement’s direction.
- Even though the item’s speed varies and its magnitude changes, the item’s direction remains the same as that of the direction of displacement.
- As displacement is less than or equivalent to the distance traveled, the quantity of average velocity is less than or equivalent to the average speed.

## AVERAGE VELOCITY FORMULA

- The formulae for the average velocity and the average speed are the same ( described in the image), but the only variation is the type of physical measure, which is speed or velocity in this case.
- Speed is a single-magnitude
**scalar**quantity. - Velocity, on the other hand, is a
**vector**quantity with both magnitude and direction. - The mathematical description of average velocity can be

**Average velocity (V) = x1 – x2 ( net displacement ) / t1 – t2 ( net time)**

An example of the average velocity can be

Example 1. In 5 hours, a truck driver travels 20 miles ( 32.18 KM) down the road. He then changes direction and travels 12 miles ( 19.3 KM) in 3 hours. What’s his average velocity?

We know v ( average velocity ) = net displacement / net time Therefore , v = (20- 12)/ (5 3 ) And finally, the average velocity will be 1 kilometer/hour.

Example 2. A car is moving along the surface OA. It moves from O to A in 18 seconds and returns A to B in 6 seconds. If OA = 360 meter and OB = 240 meter then find average velocity from – O to A and O to B.

OA = OB + AB 360 = 240 – AB AB = 120 meter

Average velocity for O to A = Total displacement / Total time = 360 m (Along OA) / 18 sec = 20 m/s (Along OA)

Average velocity for O to B **Average velocity = Total displacement / Total time**

O is the initial point and B is the final point. We will consider the shortest distance between O and A which is O and B

Average velocity = OB (Along OB) / Time OA + Time AB = 240 m (Along OB) / 18 sec + 6 sec = 10 m/s (Along OB)

The average velocity (Along O to A) is **20 m/s**The average velocity (Along O to B) is **10 m/s**

### Difference between Average Speed and Average Velocity

The primary distinction between speed and velocity is that speed is a scalar quantity that only considers distance travelled, but velocity is a vector quantity that also considers direction, and velocity depends upon displacement.

Average Speed: It is the total distance travelled divided by the total time taken to cover that distance.

Average Speed = Total distance covered / Total time taken In case of uniform motion the overall speed remains the same. Average speed is used to find out the overall speed in case of non-uniform motion.

Example: An object travels 16m in 4 seconds and then another 16m in 2 seconds. What is the average speed of the object?

Answer: D1 = 16 m T1 = 4sD2 = 16 m T2 = 2s

Total distance = D1 + D2 = 16 + 16 = 32 mTotal time taken = T1 + T2 = 2 + 4 = 6 sAverage speed = 32m / 6s = 5.33 m/s The average speed of the object is 5.33 m/s

**Average Velocity**

It is the total displacement divided by the total time taken to cover that distance.Average velocity = Total displacement / Total time

If the velocity is changing but at uniform rate than the average velocity will be arithmetic mean of initial and final velocities. In such a case we will have to use the following formula-

**Average Velocity = Initial velocity + Final velocity / 2**

Example. Usha swims in a 90 m long pool. She covers 180 m in one minute by swimming from one end to the other and back along the same straight path. Find out the average speed and the average velocity of Usha.

Answer: Total distance covered by Usha in 1 min is 180 m

Displacement of Usha in 1 min = 0 m1 minute is converted in seconds 1 min = 60 secAverage speed = Total distance covered / Total time taken = 180 m / 60 s = 3 ms-1Average Velocity = Total Displacement / Total time taken = 0m / 60s = 0ms-1

The average velocity of Usha is 0 ms-1

**Magnitude of Average Velocity**

Magnitude of average velocity of an object is equal to its average speed only when the object is moving in a straight line.

Question. In 1 second a particle goes from A to B moving in semi-circle of radius 1.0 meter. Find out the magnitude of average velocity.

Answer: Average velocity = Total displacement / Total time Average velocity = 2 m / 1 s = 2 m/sThe magnitude of average velocity of the particle is 2 m/s.

**Average Angular Velocity**

The average pace at which an object rotates over a specific period of time is referred to as its average angular velocity. Angular velocity measures how fast or how slow a body is rotating or it can be even said as how much angular displacement a body covers in one second. It is a vector quantity.

Angular velocity is denoted by Omega (ω).

Formula of Angular Velocity is ω = change in angular displacement / change in time**= (Final angular coordinate) – (Initial angular coordinate) / (Final time) – (Initial time)**

# SUMMARY

- The magnitude of an object’s velocity, regardless of direction, is called speed, and Velocity encompasses both speed and direction.
- Average velocity’s definition is the time duration of the object selected divided by the displacement in relation to the initial position.
- The formula for the average velocity and the average speed are same
**Average velocity (V) = x1 – x2 ( net displacement ) / t1 – t2 ( net time)**

## FAQs

**1. When is the average velocity zero?**

The average velocity will be zero in all the cases where the net displacement would be zero.

**2. Can average velocity be zero?**

Yes, when the net displacement is zero, the average velocity would be zero.

**3. Is Average velocity a vector or a scalar?**

Just like velocity, the average velocity has a direction and therefore is a vector quantity.

**4. How to calculate average velocity?**

Average velocity can be calculated using the formula. Average velocity (V) = x1 – x2 ( net displacement ) / t1 – t2 ( net time)

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