# 1.15 Rectilinear motion  (Page 6/6)

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## Uniform motion

Uniform motion is a subset of rectilinear motion. It is the most simplified class of motion. In this case, the body under motion moves with constant velocity. It means that the body moves along a straight line without any change of magnitude and direction as velocity is constant. Also, a constant velocity implies that velocity is constant all through out the motion. The velocity at every instant during motion is, therefore, same.

It follows then that instantaneous and averages values of speed and velocity are all equal to a constant value for uniform motion :

$\begin{array}{l}{v}_{a}=|{\mathbf{v}}_{\mathbf{a}}|=v=|\mathbf{v}|=\mathrm{Constant}\end{array}$

The motion of uniform linear motion has special significance, as this motion exactly echoes the principle enshrined in the first law of motion. The law states that all bodies in the absence of external force maintain their speed and direction. It follows, therefore, that the study of uniform motion is actually the description of motion, when no external force is in play.

The absence of external force is hypothetical in our experience as bodies are always subject to external force(s). The force of gravitation is short of omnipresent force that can not be overlooked - atleast on earth. Nevertheless, the concept of uniform motion has great theoretical significance as it gives us the reference for the accelerated or the non-uniform real motion.

On the earth, a horizontal motion of a block on a smooth plane approximates uniform motion as shown in the figure. The force of gravity acts and normal reaction force at the contact between surfaces act in vertically, but opposite directions. The two forces balances each other. As a result, there is no net force in the vertical direction. As the surface is smooth, we can also neglect horizontal force due to friction, which could have opposed the motion in horizontal direction. This situation is just an approxmiation for we can not think of a flawless smooth surface in the first place; and also there would be intermolecular attraction between the block and surface at the contact. In brief, we can not achieve zero friction - eventhough the surfaces in contact are perfectly smooth. However, the approximation like this is helpful for it provides us a situation, which is equivalent to the motion of an object without any external force(s).

We can also imagine a volumetric space, where massive bodies like planets and stars are not nearby. The motion of an object in that space, therefore, would be free from any external force and the motion would be in accordance with the laws of motion. The study of astronauts walking in the space and doing repairs to the spaceship approximates the situation of the absence of external force. The astronaut in the absence of the force of gravitation and friction (as there is no atmosphere) moves along with the velocity of the spaceship.

## Motion of separated bodies

The fact that the astronauts moves with the velocity of spaceship is an important statement about the state of motion of the separated bodies. A separated body acquires the velocity of the containing body. A pebble released from a moving train or dropped from a rising balloon is an example of the motion of separated body. The pebble acquires the velocity of the train or the balloon as the case may be.

It means that we must assign a velocity to the released body, which is equal in magnitude and direction to that of the body from which the released body has separated. The phenomena of imparting velocity to the separated body is a peculiarity with regard to velocity. We shall learn that acceleration (an attribute of non-uniform motion) does not behave in the same fashion. For example, if the train is accelerating at the time, the pebble is dropped, then the pebble would not acquire the acceleration of the containing body.

The reason that pebble does not acquire the acceleration of the train is very simple. We know that acceleration results from application of external force. In this case, the train is accelerated as the engine of the train pulls the compartment (i.e. applies force on the compartment. The pebble, being part of the compartment), is also accelerated till it is held in the hand of the passenger. However, as the pebble is dropped, the connection of the pebble with the rest of the system or with the engine is broken. No force is applied on the pebble in the horizontal direction. As such, pebble after being dropped has no acceleration in the horizontal direction.

In short, we can conclude that a separated body acquires velocity, but not the acceleration.

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