Regarding the Galilean transformation of x'=x-vt

[Ricky Pang]

Hello everyone,
I am confused with the minus sign of x'=x-vt. When there are 2 references frames called K and K' which K is at rest and K' moves to right with velocity V with respect to K. Let there is another frame which is my frame of reference called O. The vector sum of the displacement should be OK'=OK+vt which equals x'=x+vt. However, this is wrong. So, I want to ask that what is the physical meaning of the minus sign of Galilean Transformation? Besides, can we apply the concept of relative motion to derive the Galilean Transformation?

 

[Nugatory]

I am in a car moving at 100 km/hr down the road; call the frame in which I am at rest K' and the frame in which the road is at rest K. I pass a house along the road; one hour later, where is that house? It is 100 kilometers behind me, and that's what that negative sign in the $-vt$ term is saying.

More generally:
K' is moving to the right relative to frame K, so K and anything at rest in K is moving to the left with speed $v$ when considered from K'.
Consider an object that is at rest at position 0 in frame K; at time $t$ its coordinates in that frame will be $(0,t)$. However, it is moving to the left in K' so its position coordinate will become more negative with time; at time $t$ its coordinates in the primed frame will be $(-vt,t)$.

 

[PeroK]

The vector sum of the displacement should be OK'=OK+vt which equals x'=x+vt. However, this is wrong. So, I want to ask that what is the physical meaning of the minus sign of Galilean Transformation?

The minus sign means that the velocity (if positive) represents a frame moving to the right.

 

[haushofer]

Just my 2 cents: another way is to differentiate the relation x'=x-vt with respect to time t. You then see that the velocity the frame x' is moving plus v equals the velocity the frame x is moving.