Messed up classical mechanics problem:

[daqddyo1]

In Curl's initial statement, there is no change in potenial energy (gravitational or otherwise). The work done by Curl while walking to the front of the bus while it is accelerating is increasing his kinetic energy.
If he were sitting in his seat during the acceleration (the easier way), the force exerted by his seat back acting through the distance the bus accelerated would do the work necessary to increase Curl's kinetic energy.

 

[zoobyshoe]

This is really simple but I can't figure it out. I was on a bus when I thought of this:

Say I'm sitting in the back of a bus which is traveling on a flat surface, and accelerating with a constant acceleration (forward). Now I get up from my seat in the back and make my way to the front of the bus and take a seat at the front. Shortly after I sit down, the bus stops accelerating and is cruising at constant speed.
When I was walking (say at constant rate relative to the floor of the bus) I felt like I was doing work against a "fictitious" gravity force, so it felt like I gained some "potential" energy. Now that the bus is not accelerating anymore, it seems like that potential is gone and some energy is lost. Where did it go?

Curl, how fast do you estimate the bus' instantaneous velocity was when you started? How much was it when you sat down again, and how many seconds elapsed in between?