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}



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