Physics POSITION AND DISPLACEMENT
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### Topics Covered

• Introduction
• Rectilinear Motion
• Kinematics
• Reference Point
• Frame of Reference
• Position
• Path Length
• Displacement

### Introduction

=> Motion is change in position of an object with time.

text(Rectilinear Motion)

Motion of objects along a straight line, also known as rectilinear motion. For the case of rectilinear motion with uniform acceleration, a set of simple equations can be obtained.

text(Kinematics)

In Kinematics,

=> we study ways to describe motion without going into the causes of motion.

\color{purple}♣ \color{purple} " DEFINITION ALERT"
text(Point Object)

Point object in Kinematics is an object whose size is negligible compared to length of distance traveled.

Benefit of treating an object as Point Object are

We can ignore its rotation about the axis of the object

e,g, For example, a ball will be spinning while it is moving in a trajectory.

We Can ignore its vibrations

e.g. a falling water drop - may vibrate as it moves

=> Mathematically, a particle is treated as just a point, an object without extension, so that rotational and vibrational motions are not involved.

A body need not be 'small' in the usual sense of the word, in order to be treated as a particle.

For example, if we consider the distance from the Earth to the sun, with respect to the distance between them, both the Earth and the sun can be treated as point objects. We can find out a great deal about the motion of the sun, planets and other celestial bodies, without appreciable error, by treating these bodies as particles.

### Reference Point

In order to specify position, we need to use a reference point and a set of axes.

It is convenient to choose a rectangular coordinate system consisting of three mutually perpendicular axes, labelled X-, Y-, and Z- axes. The point of intersection of these three axes is called origin (O) and serves as the reference point.

### Frame of Reference

The coordinates (x, y, z) of an object describe the position of the object with respect to this coordinate system. To measure time, we position a clock in this system. This coordinate system along with a clock constitutes a frame of reference.

If one or more coordinates of an object change with time, we say that the object is in motion. Otherwise, the object is said to be at rest with respect to this frame of reference.

The choice of a set of axes in a frame of reference depends upon the situation. For example, for describing motion in one dimension, we need only one axis. To describe motion in two/three dimensions, we need a set of two/three axes.

Description of an event depends on the frame of reference chosen for the description. For example, when you say that a car is moving on a road, you are describing the car with respect to a frame of reference attached to you or to the ground. But with respect to a frame of reference attached with a person sitting in the car, the car is at rest.

### Path Length

Consider the motion of a car along a straight line. Let P, Q and R represent the positions of the car at different instants of time.

Consider two cases of motion. In the first case, the car moves from O to P. Then the distance moved by the car is OP = +360 m. This distance is called the path length traversed by the car.
In the second case, the car moves from O to P and then moves back from P to Q. During this course of motion, the path length traversed is OP + PQ = + 360 m + (+120 m) = + 480 m.

Path length is a scalar quantity — a quantity that has a magnitude only and no direction.
Q 1925156961

Look at the graphs, given below, carefully and
state the reasons which of these graphs cannot
possibly represent one-dimensional motion of
a particle.
Class 11 Exercise 3 Q.No. 16
Solution:

(a) This graph does not represent one
dimensional motion because at the given
instant of time, the particle will have two
positions, which is not possible in one
dimensional motion

(b) This graph does not represent one
dimensional motion because at the given
instant of time, the particle will have
velocity in positive as well as in negative
direction, which is not possible in one
dimensional motion.

(c) It also does not represent one-dimensional
motion because this graph tells that the
particle will have the negative speed. Never
happens.

(d) This graph does not represent one
dimensional motion because here the total
path length decreases after certain time but
total path length of a moving particle can
never decrease with time.

### Displacement

Displacement has both magnitude and direction. Such quantities are represented by vectors.

Let x_1 and x_2 be the positions of an object at time t_1 and t_2.
Then its displacement Deltax= x_2-x_1 in time (Deltat=t_2-t_1)
If x_2 > x_1, Δx is positive; and if x_2 < x_1, Δx is negative.

In one-dimensional motion, there are only two directions (backward and forward, upward and downward) in which an object can move, and these two directions can easily be specified by + and – signs.

For example, displacement of the car in moving from O to P is :
Δx = x_2– x_1= (+360 m) – 0 m = +360 m
The displacement has a magnitude of 360 m and is directed in the positive x direction as indicated by the + sign.

Similarly, the displacement of the car from P to Q is 240 m – 360 m = – 120 m. The negative sign indicates the direction of displacement. Thus, it is not necessary to use vector notation for discussing motion of objects in one-dimension.

text(Note:)
• The magnitude of displacement may or may not be equal to the path length traversed by an object.
• The magnitude of the displacement for a course of motion may be zero but the corresponding path length is not zero.

### Uniform Motion

If an object moving along the straight line covers equal distances in equal intervals of time, it is said to be in uniform motion along a straight line. Fig. (b) shows the position-time graph of such a motion.