Final answer:
The rate of change at a point p in the direction of vector u is known as the directional derivative, which is calculated using calculus and vector analysis.
Step-by-step explanation:
The rate of change of a function at a point p in the direction of a vector u is referred to as the directional derivative. In physics, when considering motion, u often represents a velocity vector, hence the directional derivative can be understood as how quickly a quantity is changing as one moves in the direction of u. Fundamentals from calculus and vector analysis are typically employed to find this directional derivative, which is often represented by the gradient of the function dotted with the vector u.
For example, consider a scenario with two observers, where u is the velocity of an object relative to one observer, and u' is the velocity relative to another observer. If both are measuring some rate of change, like velocity or momentum (which is the product of mass and velocity), they would use the object's velocity vector in their respective frames of reference to calculate the rate of change they observe.
In the given context where specific equations or details may not be provided, understanding the directional derivative or rate of change requires knowing the function which describes the system (say, pressure or momentum) then applying calculus operations to find how this function changes in the direction of u.