Average Speed and Average Velocity

Speed during a certain interval of time can not be used to determine total distance covered in given time of the journey and also the time taken to cover the total distance of journey. It is because a body does not always travel equal distance in equal interval of time.

In most of the cases the body travels non-uniformly. Thus, in case of non-uniform motion to determine average speed is quite useful. The average speed can be determined by the ratio of total distance covered to the total time taken.

Average speed = total distance covered / total time taken

Similarly, in case of average velocity in place of total distance covered you can take total displacement.

Average velocity = total displacement / total time taken

Example 1: If a body covers 50 m distance in 30 s and next 100 m in 45 s then total distance covered

= 50 + 100 = 150 m

and total time taken = 30 + 45 = 75 s

Average speed = 150 m / 75 s = 2 ms–1

Example 2: If an object moves with the speed of 10 ms–1 for 10 s and with 8 ms–1 for 20 s, then total distance covered will be the sum of distance covered in 10 s and the distance covered in 20 s

= 10 × 10 + 8 × 20 = 260 m

The average speed = total distance covered / total time taken

= 260 m / (10+20 s) = 260 m / 30 s

= 8.66 ms–1

Example 3: If a body moves 50 m with the speed of 5 ms–1 and then 60 m with speed of 6 ms-1, then total distance covered

= 50 + 60 = 110 m

and total time taken will be the sum of time taken for 50 m and 60 m = 20 s

Thus, average speed = total distance covered / total time taken

= 110 m / 20 s

= 5.5 ms–1

Example 4: If an object moves 30 m toward north in 10 s and then 40 m eastward in next 10 s, the displacement of the object will be

OB = √(302 + 402) = √(900 + 1600) = √2500

= 50 m

The average velocity = total displacement covered / total time taken

= 50 m / (10+10 s)

50 m / 20 s

= 2.5 ms–1

Example 5: If an object moves along a circular track of radius 14 m and complete one round in 20 s then for one complete round total displacement is zero and the average velocity will also be zero.

From these examples you can conclude that:

1. Instantaneous speed is the magnitude of instantaneous velocity but average speed is not the magnitude of average velocity.
2. Average velocity is less than or equal to the average speed.
3. Average velocity can be zero but not average speed.