# CONTENTS Chapter 2 ... ON MOTION

Article 20 ... Definition of Displacement
Article 21 ... Diagram of Displacement
Article 22 ... Relative Displacement
Article 23 ... Uniform Displacement
Article 24 ... On Motion
Article 25 ... On the Continuity of Motion
Article 26 ... On Constant Velocity
Article 27 ... On the Measurement of Velocity when Variable
Article 28 ... Diagram of Velocities
Article 29 ... Properties of the Diagram of Velocities
Article 30 ... Meaning of the Phrase "At Rest"
Article 31 ... On Change of Velocity
Article 32 ... On Acceleration
Article 33 ... On the Rate of Acceleration
Article 34 ... Diagram of Accelerations
Article 35 ... Acceleration a Relative Term

## Article 20 - Definition of Displacement

We have already compared the position of different points of a system at the same instant of time. We have next to compare the position of a point at a given instant with its position at a former instant. called the Epoch

The vector which indicates the final position of a point with respect to its position at the epoch is called the Displacement of that point. Thus if A1 is the initial and A2 the final position of the point A, the line A1A2 is the displacement of A, and any vector OA drawn from the origin O parallel and equal to A1A2 indicates this displacement.

## Article 23 - Uniform Displacement

When the displacements of all points of a material system with respect to an external point are the same in direction and magnitude, the diagram of displacement is reduced to two points - one corresponding to the external point, and the other to each and every point of the displaced system. In this case the points of the system are not dipslaced with respect to one another, but only with respect to the external point.

This is the kind of displacement which occurs when a body of invariable form moves parallel to itself. It may be called uniform displacement.

## Article 24 - On Motion

When the change of configuration of a system is considered with respect only to its state at the beginning and the end of a process of change, and without reference to the time during which it takes place, it is called the displacement of the system.

When we turn our attention to the process of change itself, as taking place during a certain time and in a continuous manner, the change of configuration is ascribed to the motion of the system.

## Article 25 - On the Continuity of Motion

When a material particle is displaced so as to pass from one position to another, it can only do so by travelling along some course or path from the one position to the other.

At any instant during the motion the particle will be found at some one point of the path, and if we select any point of the path, the particle will pass that point once at least during its motion.

This is what is meant by saying that the particle describes a continuous path. The motion of a material particle which has continued existence in time and space is the type and exemplar of every form of continuity.

## Article 30 - Meaning of the Phrase "At Rest"

It is true that when we say that a body is at rest we use a form of words which appears to assert something about that body considered in itself, and we might imagine that the velocity of another body, if reckoned with respect to a body at rest, would be its true and only absolute velocity. But the phrase "at rest" means in ordinary language "having no velocity with respect to that on which the body stands", as, for instance, the surface of the earth or the deck of a ship. It cannot be made to mean more than this.

It is therefore unscientific to distinguish between rest and motion, as between two different states of a body in itself, since it is impossible to speak of a body being at rest or in motion except with reference, express or implied, to some other body.

## Article 35 - Acceleration a Relative Term

Acceleration, like position and velocity, is a relative term and cannot be interpretted absolutely. If every particle of the material universe within the reach of our means of observation were at a given instant to have its velocity altered by compounding therewith a new velocity, the same in magnitude and direction for every such particle, all the relative motions of bodies within the system would go on in a perfectly continuous manner, and neither astonomers nor physicists, through using their instruments all the while, would be able to find out that anything had happened. It is only if the change of motion occurs in a different manner in the different bodies of the system that any event capable of being observed takes place.

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