On the least uncomfortable journey from A to B

Abstract

The problem of the "least uncomfortable journey" between two locations on a straight line, originally discussed by Anderson {\it et al.} (2016 {\it Am. J. Phys.} {\bf 84} 6905) is revisited. When the integral of the square of the acceleration is used as a measure of the discomfort, the problem is shown to be easily solvable by taking the time, instead of the position, as the independent variable. The solution is quite simple and avoids not only complicated differential equations and the computation of cumbersome integrals, but also the inversion of functions by solving cubic equations. Next, the same problem, but now with the integral of the square of the jerk as a measure of the discomfort, is also exactly solved with time as the independent variable and the appropriate boundary conditions, which are derived. It is argued that the boundary conditions imposed on the velocity in Anderson {\it et al.} (2016 {\it Am. J. Phys.} {\bf 84} 6905) are inappropriate not only because they are not always physically realizable but also because they do not lead to the minimum discomfort possible.