# Chapter : Rest and Motion

Simple pendulum(image source: wikipedia.org)In our daily life we see many objects that are either in rest position or Motion. eg- moving Trains, car ,cycle, etc and on other hand trees, houses, furnitures, etc are in rest position.

## Rest :-

If any object does not change its position with respect to time and its surroundings, then it is called at rest.## Motion:-

If the position of any objects changes with the time and its surroundings, then it is said to be at the state of motion.## Types of motion

### Rectilinear and Translatory motion :-

If a body travels in a straight line, horizontally or vertically, then the motion is called rectilinear or Translatory motion. eg - motion of a car in straight line, falling of a object from some height.

### Circular Motion :-

when a body moves along a circular path, then its motion is called circular motion. In circular motion a body always accelerated towards the gravity.### Periodic Motion :-

The motion which repeats itself after a regular interval of time is called periodic motion. eg - movement of hands in a clock.

### Simple Harmonic Motion :-

If a body moves to and fro in a straight line about a fixed point or position, then the motion of the body is called Simple Harmonic Motion. eg - movement of a pendulum.### Oscillatory Motion :-

If a body repeats its movement after a regular interval of time about a fixed point, then the motion is called Oscillatory motion.### Projectile Motion :-

Projectile motion is a form of motion in which an object or particle is thrown near the earth’s surface, and its moves along a curved path under the action of gravity. The path of projectile is always parabolic.For the maximum range of the projectile, the angle of projection should be 45°.

For maximum height of the projection, the angle of projection should be 90°.

## Simple Pendulum :-

A simple Pendulum i s a point mass suspended from rigid support by means of an elastic inextensible string.
Time period of a simple pendulum depends on the length of the string, which is known as effective length, and the acceleration due to gravity.

t = 2 π√l/g

Where l = length of the string and g = acceleration due to gravity.

Where l = length of the string and g = acceleration due to gravity.

Time period of a simple pendulum is independent of the mass of the bob which is suspended.

## Some Basic Terms related with Motion

### Distance :-

The length of the path covered by a body in a particular time interval is called diatanced.
Distance is always positive and its unit is meter (m). It is a scalar quantity.

### Displacement :-

The shortest distance between the initial and final points in a particular direction is called displacement.
It can be negative, zero or positive. Its unit is also meter (m). It is a vector quantity.

### Speed :-

The rate of change of distance is called speed.
Mathematically, speed = distance/time.

It is a scalar quantity and its unit is m/s.

It is a scalar quantity and its unit is m/s.

### Velocity :-

The rate of change of displacement is called velocity, i.e. Velocity = displacement/time.It is a vector quantity and its unit is also m/s.It may be negative, zero or positive.

### Uniform velocity :-

If a body covers equal displacements in equal interval of time, then it is said that the body is moving with uniform velocity.### Non-uniform Velocity :-

If a body covers unequal displacement in equal intervals of time, then it is said that the body is moving with non-uniform velocity.

### Acceleration :-

It is the rate of change of velocity.It is a vector quantity. Its S.I. unit is m/s.
It may be negative, zero or positive.

If it is positive, then it is known as acceleration. If it is zero, then the body is moving with a uniform velocity. If it is negative, then it is known as retardation.

If it is positive, then it is known as acceleration. If it is zero, then the body is moving with a uniform velocity. If it is negative, then it is known as retardation.

## Equations of Motion

v=u+at

s=ut+1/2at²

v²=u²+2as

Where, s = distance or displacement covered by the body

v = final velocity

u = initial velocity

t = time period

a = acceleration