The "x'=x-vt" in Galilean/Lorentz transformation

[JohnTitor]

Hello people,
I have a question regarding the x' component in the Lorentz/Galilean transformation.
So from what i understand is that there are 2 coordinate systems used in the transformations. One is used as a reference point and one is used for moving away from this point. The moving away in x-axis is described with x'=x-vt but where does the "-vt" come from and why is it "minus vt" and not "positive vt"?

Is the sign determined by how the prime(')-coordinate system moves relative to the other system? (So it's -vt when you move against the direction of the x-axis?)

 

[Mentz114]

You can work out the direction of motion by checking if x' increases or decreases with t.

 

[Ibix]

You can draw a displacement-time graph for a pair of objects moving at speed v. What is the equation of the line in terms of x and t? Can you relate x' to this? Drawing an x' vs t graph may help with the latter.

 

[Chestermiller]

Hello people,
I have a question regarding the x' component in the Lorentz/Galilean transformation.
So from what i understand is that there are 2 coordinate systems used in the transformations. One is used as a reference point and one is used for moving away from this point. The moving away in x-axis is described with x'=x-vt but where does the "-vt" come from and why is it "minus vt" and not "positive vt"?

Is the sign determined by how the prime(')-coordinate system moves relative to the other system? (So it's -vt when you move against the direction of the x-axis?)

It's geometric. The S' frame is moving with positive velocity v relative to the S frame. Draw a picture showing the location of the S' frame relative to the S frame at two different times, and you will see visually how this plays out.

Chet