The discussion clarifies the distinction between differentiation and partial differentiation in the context of physics. The equation for gravitational acceleration, g = GM/r², is established as a fundamental concept, where g represents acceleration due to gravity. The basic definition of acceleration is given as a = dv/dt, which applies to various forces, not solely gravity. Partial differentiation is relevant only when multiple independent variables are present, making it unnecessary in introductory physics focused on time as the sole variable.
PREREQUISITESStudents of physics, educators teaching calculus-based physics, and anyone seeking to deepen their understanding of differentiation in physical contexts.
Redbelly98 said:g = GM/r^2 gives the acceleration due to gravity.
a = dv/dt is the basic definition of acceleration (which can be cause be any other force, not just gravity)
Partial differentiation is used when there are more than one independent variables. But since the study of motion in introductory physics uses just one independent variable -- time -- partial derivatives are not relevant.