# Average velocity and Average speed.

Average velocity:
Average velocity is the measure of the average change of position of an object in any given time interval.
Mathematically,
Average velocity = $v_{avg} = \frac{\Delta x}{\Delta t} = \frac{x_2 - x_1}{t_2 - t_1}$

Where , $\Delta x$ = Total change in position , $\Delta t$ = total time interval. $x_2 , x_1$ = position of the object at two different time and $t_2 , t_1$ = Different time.

Average velocity does not depend on the actual path followed by the object , It only depends on the initial and final position of the object in a time period.

If we draw a graph “x” versus “t”  for the motion of an object; where , “x” = position of an object and “t” = time.

Then the average velocity of the object in a given time interval is the slope of the line joining it’s initial and final position in the time interval.

Average Speed:

The average speed of a particle during a time interval $\Delta t$ is the average distance moved by the particle during the time interval.

Mathematically,

Average speed = $s_{avg} = \frac{Total \, \, distance \, \, moved}{\Delta t}$

Example:

Let us suppose a vehicle which is moving in a strange way.

Let, at different time the vehicle is at different position from its starting point.

And let us also suppose the movement of vehicle in a direction as positive and in the opposite direction as negative, and the data for its position at different time is:

At time 0 second , it is at the origin.

At time 1 second, it is 1 meter far from the origin.

At time 2 second, it is 2 meter far from the origin.

At time 3 second, it is 7 meter far from the origin.

At time 4 second, it is 5 meter far from the origin.

At time 5 second, it is 10 meter far from the origin.

So we can analyze above data and come into following conclusion:

In the first second the vehicle moved 1 meter in positive direction.

In the second second the vehicle moved 1 meter in positive direction.

In the third second it moved 5 meters in positive direction.

In the fourth second it moved 2 meters in negative direction.

And in the last second it moved 5 meters in positive direction.

In the above example ,

the average velocity of the vehicle = $\frac{(10 -0) m}{(5-0)} = 2 ms^{-1}$

But the average speed of the vehicle = $\frac{(1+1+5+2+5) m}{(5-0)} = 2.8 ms^{-1}$

Related posts:

1. Position and Displacement. Position of an object is its location. and Displacement is...
2. Motion. Motion is the process of changing of position by an...
3. Standards of Measurement: Length , Mass and Time. The laws of physics are expressed as mathematical relationships among...
4. The Chain Rule. Chain Rule is one of the Techniques of Differentiation. The...
5. Derivative of simple algebraic or polynomial functions. The derivative and calculations on finding derivative of simple algebraic functions...