The Reciprocal Velocity Force of a Transmission

The reciprocal velocity force, $F(v)=\frac{C}{v}$, despite its theoretical and practical importance, is often neglected in mechanics courses. We use graphical methods to explain how such a force naturally arises from a device called a transmission, and discuss the kinematic consequences of this force. As an application, we discuss the role of this force for both internal combustion engines and electric vehicles.