 # Average Velocity and Average Speed

Suppose an object is in motion, the position of that object changes with time. But how fast is the position changing with time and in what direction? To understand this, we define average velocity and average speed.

### Suggested Videos        ## Average Velocity

Average velocity is the ratio of total displacement to total time. Its direction is the same as the direction of the moving object. Even if the object is slowing down, and the magnitude of the velocity is decreasing, its direction would be still the same as the direction in which the object is moving. The magnitude of average velocity is always less than or equal to the average speed because displacement is always smaller than or equal to distance. It is a vector quantity and has units of m/s

Average velocity = $$\frac{Total Displacement}{Total Time}$$

The average velocity of the particle can be positive as well as negative and its positive and negative value depends on the sign of displacement. If the displacement of the particle is zero its average velocity is also zero.

### Calculating Average Velocity

The velocity of a particle is :

$$\vec{v} = \frac{d \vec{x}}{dt}$$

## Average Speed

The total distance travelled by the body in total time is the average speed.

Average speed = $$\frac{Total Distance}{Total Time}$$

It is a scalar quantity and its units are m/s.

### Calculating Average Speed

Average speed is found by the first finding the total distance covered by the object and dividing it by the total time taken in travelling the distance. Example: A body covers a circle of radius 100m on 100s, implies the total distance covered by him will be d = 2πr = 200π m. So, the average speed will be v= $$\frac{d}{t}$$ = 2π m/s

If the motion of an object is along a straight line and in the same direction, the magnitude of displacement is equal to the total path length. In that case, the magnitude of the average velocity is equal to the average speed. In case the average speed is not equal to the magnitude of the average velocity, this is because the motion involves a change in direction and so path length is greater than the magnitude of displacement. So the average speed is greater than the magnitude of the velocity.

Learn how to calculate Instantaneous Speed and Velocity here

## Solved Examples For You

Q. A particle moves for 20swith velocity 3m/s and then moves with velocity 4m/s for another 20s and finally moves with velocity 5m/s for next 20s what is the average velocity of the particle? (in m/s)

1. 3
2. 5
3. 4
4. zero

Q.2 An insect crawling straight down the length of a meter stick is at the 12cm mark at one instant, and 22 minutes later is at the 60cm mark. Which one of the following is the magnitude of the insect’s average velocity?

1. 0.4cm/s
2. 0.5cm/s
3. 24cm/s
4. 30cm/s

Answer: A. The total displacement of insect is S= 60-12 =48cm

Total time taken t= 2min =120s

Insect’s average velocity =  $$\frac{48}{120}$$ = 0.4 cm/s

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