If the speedometer of a bus shows 20 km/h then this speed is called instantaneous speed. If we further add to this information that the bus is traveling northwards, then we say that its instantaneous velocity is 20 km/h northwards.
The magnitude of the Speed and Velocity is the same here - 20km/hour. But the instantaneous Velocity has one addition information- the direction of the motion of the bus.
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 the 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.
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.
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.
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.
[Contributed by administrator on 10. Januar 2018 21:46:47]
Calculating Velocity
Velocity can be instantaneous or average.
If the speedometer of a bus shows 20 km/h then this speed is called instantaneous speed. If we further add to this information that the bus is traveling northwards, then we say that its instantaneous velocity is 20 km/h northwards.
The magnitude of the Speed and Velocity is the same here - 20km/hour. But the instantaneous Velocity has one addition information- the direction of the motion of the bus.
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 the 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.
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.
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.
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.