Integrating Velocity: Questions on Displacement & Position

[opus]

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.

 

[andrewkirk]

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.

 

[opus]

Ok thank you, so then is it possible to find exactly the position of $x$ when we have the graph of velocity?

 

[PeroK]

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.

 

[opus]

Understood! Thank you.

 

[Neeraj Chandran]

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

 

[opus]

Excellent thank you.