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Chapter 2: Problem 3

You check your odometer at the beginning of a day's driving and again at the end. Under what conditions would the difference between the two readings represent your displacement?

Short Answer

Expert verified
The difference between two odometer readings would represent displacement when the vehicle is traveling in a straight line without changing its direction.

Step by step solution

01

Understand Displacement and Distance

Displacement is a vector quantity that refers to the shortest distance from the initial to the final position of a point. It includes both the length and direction of that shortest path. On the other hand, the distance you see on an odometer is a scalar quantity. It is the total distance traveled by an object, regardless of the direction.
02

When Distance Equals Displacement

The difference between two odometer readings would represent displacement when the vehicle is traveling in one straight path without changing direction. In other words, if you started driving from point A, drove in a straight line without any turns, and stopped at point B, then the odometer reading would equal the displacement.
03

Contrast with a Non-linear Path

If the vehicle takes a non-linear path or returns to the start point, the odometer reading will be greater than the displacement (which could even be zero if the vehicle returns to the start). An odometer measures the total distance travelled, not the net change in position, so it doesn't account for changes in direction.

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