Integrating Velocity: Questions on Displacement & Position

In summary, when we integrate velocity, we get the displacement of ##x## and this can be found by setting the limits of the time interval and finding the equation of displacement with respect to time. By setting the initial time to 0, we can also find the position from the origin.
  • #1
opus
Gold Member
717
131
Please see the attached image which are of my notes. In integrating acceleration, I have no confusions. But I have a specific question about integrating velocity.

When we integrate velocity, do we get the displacement of ##x##, or do we get it's position at a certain time?
I want to say it's the displacement as it's directly in the definition in green and integration is basically accumulated area. But I want to be sure.
Thank you.
 

Attachments

  • Screen Shot 2019-01-10 at 11.10.34 PM.png
    Screen Shot 2019-01-10 at 11.10.34 PM.png
    21.9 KB · Views: 433
Physics news on Phys.org
  • #2
Yes it's the displacement. If the velocity is a scalar (one-dimensional motion) it's a simple positive or negative displacement. If it's a 2D or 3D velocity vector, we integrate each coordinate separately and get an overall 3D displacement vector as the result. Adding the displacement vector to the starting point in an affine sense gives us the position at the end of the journey.
 
  • Like
Likes opus
  • #3
Ok thank you, so then is it possible to find exactly the position of ##x## when we have the graph of velocity?
 
  • #4
opus said:
Ok thank you, so then is it possible to find exactly the position of ##x## when we have the graph of velocity?

If you know the starting position and you know the displacement, then you know the current position.
 
  • Like
Likes opus
  • #5
Understood! Thank you.
 
  • #6
opus said:
Please see the attached image which are of my notes. In integrating acceleration, I have no confusions. But I have a specific question about integrating velocity.

When we integrate velocity, do we get the displacement of ##x##, or do we get it's position at a certain time?
I want to say it's the displacement as it's directly in the definition in green and integration is basically accumulated area. But I want to be sure.
Thank you.
Actually during integration we set two limits t1 and t2 so that we get the displacement between the 2 time interval. After integration we gets the equation of displacement(with respect to time) of a particle . And when we sets the limit we get the displacement during that particular time interval. To find the actual position from origin you have to put t1=0. So we get its position as well as displacement from the origin. Thank you
 
  • Like
Likes opus
  • #7
Excellent thank you.
 

What is displacement?

Displacement is the distance and direction of an object's change in position from its starting point. It is a vector quantity, meaning it has both magnitude (size) and direction.

How is displacement different from distance?

Distance is the total length traveled by an object, while displacement is the straight-line distance and direction between an object's starting and ending points.

What is position?

Position refers to the location of an object in relation to a reference point. It can be described using coordinates or a reference system.

How is position related to displacement?

Position is the starting point for calculating displacement. Displacement is the change in position from the starting point to the ending point.

What is the formula for calculating displacement?

The formula for calculating displacement is: displacement = final position - initial position. This can also be written as Δx = xf - xi, where Δx is displacement, xf is final position, and xi is initial position.

Similar threads

Replies
4
Views
906
Replies
8
Views
710
Replies
49
Views
1K
Replies
4
Views
829
Replies
19
Views
1K
Replies
4
Views
884
Replies
3
Views
1K
Replies
15
Views
864
Replies
69
Views
2K
Replies
4
Views
7K
Back
Top