Calculating Velocity

Like speed Velocity can be instantaneous or average.

In the video given below, please look at the speedometer and note the changes it shows carefully.

The speedometer was showing the speed in km/hour. As the bus was moving, the needle of the meter was showing the speed at that particular moment. This is called the instantaneous speed, or the speed at that moment. If we add that the bus is travelling northwards, we are now talking about velocity of the bus. Velocity has both components - magnitude i.e. speed and, direction, which here is the north direction.
 
So if at 8.10 a.m., needle of the speedometer was at 20 km mark on the speedometer dial, we will say that instantaneous velocity of the bus at 8.10 a.m. was 20 km/hour in north direction. At 8.11 a.m., if the needle moves to 25 km mark, then the instantaneous velocity has changed to 25 km/hour in north direction.
 

The path between the two points (two places) could be as short as straight or long and winding. To work out the Average speed - you need to know the distance (the actual length of the path) and the team takes to cover this distance. 
 

But for the Average Velocity you just want to know the displacement between these two points. the time it takes to move between these points. 
 

You already know that for straight line motion, the Displacement work out to be the shortest distance (straight line) in the direction of Point B to Point A.
 

Let us learn how do we calculate the average velocity?

The average velocity of an object is the distance covered by the object in a unit of time in a particular direction – or its displacement in a unit of time.

The equation of average velocity is as follows:

                                                              Average velocity  \(V = {Displacement \over Total~ time~taken}\)

Now, consider the motion of Lily again and calculate her speed and velocity.





She starts her journey from point A, so point A becomes the initial point. She goes to B from A, then she comes back to A from B and walks to C from A.

Suppose she takes 1 second to walk 1 meter. So, her speed will be 1 meter/second.

(i) For Journey from A to B:

She travels a distance of 50 meters  from A to B. As her speed is 1 meter/second, that means she will take total 50 seconds to cover a distance of 50 meters.

Her velocity would be 1 m/s in the direction of the line AB.

So the magnitude of velocity and speed are the same for this part of the journey.

(ii) For Journey A to B and back to B to A:

For this part of the journey, her displacement is zero because she begins to walk from A and goes to B and comes back to A again. But she covers a distance of 100 meters.

Her velocity would be zero meter/second while speed would be 1 meter/second.

(iii) For Journey A to B and back to A to C :
 

When she goes to C crossing initial position, she covers a distance 150 meters but her displacement will be 50 meters leftwards.

Again the speed will be 1 m/s but her velocity will be different as the displacement is only 50 m leftwards (or -50 meters).
 

Using the equation of average velocity,
                                                                                     

                                                          Average velocity  \(V = {Displacement \over Total~ time~taken}\)

                                                                                                      V = 50m/150 s

                                                                                                       V  = 0.33 m/s  left wards, or 
                                                       
                                                                                                       V = -0.33 m/s (negative sign shows the direction)

In this case the velocity is 0.33 m/s leftwards but the speed is 1 m/s.