## Average velocity formula

Average velocity is the distance travelled by a body in time t. It is denoted by V_{av}.

### Average Velocity

The rate of displacement made by an object with time is known as average velocity. The direction of average velocity is the same as that of the direction of displacement. The change in the speed of the object and the magnitude of fluctuations does not disrupt the direction of displacement of the object.

The magnitude of average velocity is always less than or equal to the average speed. The displacement is also always less than or equal to the distance covered.

For example, an athlete who runs 5 miles north is likely to change his velocity at certain times during the run. The average velocity of the athlete can easily be calculated by dividing the change in position of the athlete (5miles) by the total time of the run.

## Calculation Of Average Velocity

Total Displacement ÷ Total Time

Calculation of Average Velocity when final velocity ‘V’ is given and Initial velocity ‘U’ is known:

V_{uv} = (U + V) / 2

Calculation of average velocity when diverse distances d_{1}, d_{2}, d_{3} ….. d_{n} and diverse time intervals t_{1}, t_{2}, t_{3}…. t_{n} are given:

V_{av} = (d_{1} + d_{2} + d_{3} +….. d_{n}) ÷

(t_{1} + t_{2} + t_{3} +….t_{n})

### Most Commonly Units Used To Denote Velocity

International system- kilometres per hour (km/h)

International system- metres per second (m/s)

English system- miles per hour (mph)

English system- Feet per second (ft/s)

## Solved Examples

**Question- Calculate the average velocity of a car whose initial velocity is 30 m/s and final velocity is 80 m/s. **

**Answer-** U = 30 m/s

V = 80 m/s

V_{av} = (U + V) / 2

V_{av }= (30 + 80) / 2

V_{av} = 55 m/s

**Question- Calculate the average velocity of runners if a runner is running at 10 mph at the start of the run and 7.5 mph at the end of it. **

**Answer-** Initial Velocity = 10 mph

Final velocity = 7.5 mph

V_{av} = (U + V) / 2

= (10 + 7.5) / 2

= 8.75 mph

Therefore the average velocity of runners is 8.75 mph.

**Question- Calculate the average velocity of a driver who is driving 20 km down the road in 5 minutes. He reverses his car and drives 12 km in 3 minutes. **

**Answer- **

V = D/t

V = (20-12) ÷ (5+3)

= 8÷8

= 1 kilometre per minute