# Under the Lantern

Mia is standing under one of the lanterns which are in front of her house in a distance of 20 meter to each other. She is waiting there to be picked up by her girlfriend. It takes some time and so she is puttering around.

According which time-speed-graph will she be farthest away from her starting point?

## Answer

The answer is: d)

According the v(t)-graphs a) to c) Mia is puttering only around the first lantern, but does not really move away from it.

On graph d) she moves to the next lantern in a distance of 20 m. There she is waiting in the hope that she will be picked up earlier.

### „Lamppost walk“

Such a movement back and forth around a mean value or the movement away from its initial value play a role in statistical physics as to show the ramdom change of a quantity.

A popular intellectual game is the „Lamppost walk“: A drunkard starts at a lantern. Each of his steps has a certain length. But the man is so drunk, that it is at each time entirely open whether he does a step forward or backward. The move into the one direction can be more likely as into the opposite direction. Does the street, for example, rise steeply, a step downward is obviously more likely than a step upward.

The principle of random oscillations is fundamental for the theory of probability and is applied in all field of physics.