Different Speeds Observed in Different Frames

This section describes the dependency of speed on the frame of reference. selecting different frames of reference will result different speeds of the same moving object.

To calculate the speed of a moving object, we need to measure the distance the object has moved within a give duration of time. To measure the distance the object has moved, we need a frame of reference.

This means that selecting different frames of reference will result different speeds of the same moving object. Let's consider the following example.

An archer is going to shoot two arrows to a target. The first arrow will be shot from ground and the second shot from a truck that moves towards the target.

Let's assume that we have a frame of reference fixed on the ground called "x1", and another frame of reference fixed on a truck called "x2".

When the archer stands on ground and shoots the first arrow, we observe that arrow flies 20 meters from A to B in frame x1 for 1 second. So the speed of the arrow is v1 = 20 m/s in frame x1 when shooting from the ground.

Now the archer climbs to the truck that moves towards the target at a speed of 10 m/s observed in frame x1, shoots the second arrow. This time, we can make two observations:

So the speed of the arrow has 2 values:

Different Speeds Observed in Different Frames
Different Speeds Observed in Different Frames

Last update: 2014.

Table of Contents

 About This Book

 Introduction of Space

 Introducion of Frame of Reference

 Introducion of Time

Introduction of Speed

 What Is Speed?

 List of Various Speeds

Different Speeds Observed in Different Frames

 Measuring Speed of Light - Roemer's Method

 Measuring Speed of Light - Fizeau's Method

 Measuring Speed of Light - Foucault's Method

 Newton's Laws of Motion

 Introduction of Special Relativity

 Time Dilation in Special Relativity

 Length Contraction in Special Relativity

 The Relativity of Simultaneity

 Introduction of Spacetime

 Minkowski Spacetime and Diagrams

 References

 PDF Printing Version