A Note on Notation

In the previous video (and in the next) you saw the following equation:

x' = x + \dot{x}

Translated into plain speech, this says

the x position after motion (x') is equal to the x position before motion (x) plus the velocity in the x direction (\dot{x}).

If you read through that statement, you might notice that it doesn't quite make sense because it doesn't take into account the duration of motion. If I drive for 10 seconds I go farther than if I only drive for 1 second!

In the previous video we are assuming that the duration of motion (typically called \Delta t) is equal to 1 second. The "complete" version of the equation above would be

x' = x + \dot{x} \Delta t