Final answer:
In physics conventions, the variable 'u' is generally used to represent the velocity of an object relative to an observer, while 'u'' is used for the velocity relative to another observer.
Step-by-step explanation:
According to convention, the variable u often stands for the velocity of an object relative to an observer, particularly in situations involving relative motion and relativity. This is contrasted with the variable v, which is typically used to represent the relative velocity between two observers or frames of reference. The notation u' is then used to denote the velocity of the same object relative to a second observer, moving with respect to the first one.
For example, in physics and particularly in the study of relativity, if we have two observers, and one is moving at a velocity of u relative to some reference frame, someone who is moving at a velocity v relative to the first observer would measure the object's velocity as u'. At low velocities, the formula u = (v+u')/(1 + vu'/c²) approaches classical velocity addition, where c is the speed of light.