Newton didn’t know about the subtle features of time as measured by clocks in motion, and would simply have said that clocks in a moving frame are all in synch with themselves and with our clocks in the laboratory. However, Newton would agree, of course, that if a given point $P$ is viewed from the perspective of a frame that’s in motion, then the spatial coordinates of $P$ in the moving frame will change over time. Let’s work out a simple example of this.

Let $P$ be the point $(2,5)$ in $(x,y)$ coordinates, and to be concrete assume the units are meters. Let the $(x^\prime , y^\prime )$ coordinate system align with the $(x,y)$ system at $t=0$, but then move to the right (along the x-axis) with a speed of 3 meters per second. At $t=$4 seconds, what would Newton say are the coordinates of P in the moving system?

Let $Q$ be the point $(10,3)$ in $(x,y)$ coordinates, and to be concrete assume the units are meters. Let the $(x^\prime,y^\prime)$ coordinate system align with the $(x,y)$ system at $t=0$, but then move to the left (along the $x$-axis) with a speed of 2 meters per second. At $t = 6$ seconds, what would Newton say are the coordinates of $P$ in the moving system?