Time Scale for Velocity to Track a Force
Chris L. Lin

TL;DR
This paper derives a formula for the time required for a force to significantly change an object's velocity direction, considering viscous effects and generalizing to other vector quantities with constant derivatives.
Contribution
It provides a new analytical expression for the velocity turn-around time under constant and viscous forces, extending to general vector quantities.
Findings
Derived formula for velocity change time $ au$
Viscous forces reduce $ au$ logarithmically
Generalization to any vector with constant first derivative
Abstract
In this paper we derive and discuss the time it takes for a force to turn a velocity. More precisely, we derive the formula for the time it takes a constant force that makes an angle with the initial velocity to have get within an angle of the force. We then show how the addition of a viscous force decreases logarithmically. The result can be generalized to any vector quantity whose first time derivative is a constant.
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