# Uniform Motion

In our daily life we see some objects in motion e.g., walking men, moving cars, running trains, and some objects at rest e.g., furnitures, houses, trees, etc. In both the cases, we see that in motion, the position of objects change with time while at rest, the position of obiects do not change with time.

## Rest

If an object does not change its position with respect to its surroundings with time, then it is called at rest. e.g., a book lying on a desk is at rest, because its position with respect to the desk does not change with time.

## Motion Class 9

If an object changes its position with respect to its surroundings with time, then it is called in motion. e.g., fish swims in water, car or bus moves on a road, train moves on the track, bird flying in air, etc.

• Rest and motion are relative terms i.e., an object in one situation can be at rest but in other situation same object can be in motion.     e.g., if two cars are going side by side with the same velocity, then with respect to each other, they are in a state of rest, but with respect to trees and persons going on the road, they are in a state of motion.

## Types of Motion of a Body

### Rectilinear Motion

The motion in which a particle moves along a straight line, is called rectilinear motion. If a body (or a particle) moves along a straight line, then the motion is called translatory motion.

### Circular and Rotatory Motion

The motion in which a particle moves along a circular path, is called circular motion. If a body rotates about a line (axis) passing through it then the motion is called rotatory motion or rotational motion.

### Oscillatory Motion

The motion in which a body moves to and fro or back and forth repeatedly about a fixed point, is called oscillatory motion (the extent to which the body moves on either side of the fixed point is called the amplitude). If in oscillatory motion, the amplitude is very small, then the motion is said to be vibratory motion.

## One, Two and Three Dimensional Motion

One-Dimensional Motion When the Everyday Science position of the object changes only in one direction , then the motion of an object is called  one dimensional motion.

OR

When a body moves along a line, then the motion is called one dimensional motion.

Two-Dimensional Motion When the position of the object changes in two direction , then the motion of an object is called two -dimensional motion.

OR

When a body moves on a plane, then the motion is called two-dimensional motion

Three-Dimensional Motion When the position of the object changes in three direction, then the motion of an object is called three-dimensional motion.

OR

When a body moves in a space, then the motion is called three-dimensional motion.

## Some Basic Terms Related with Motion

The various terms required to describę motion are

### Reference Point

A fixed point or a fixed object with respect to which the given body changes its position is known as reference point or origin.

• An object is said to be in motion, if its position changes continuously with respect to a fixed reference.

### Position

It is the point in space where an object is present with respect to the reference point.

### Distance

Distance The distance travelled by a body is the actual length of the path covered by a moving body irrespective of the direction in which the body travels. It is a scalar quantity. Its Its SI Unit is metre.

•  Odometer is a device used to measure the distance travelled by the vehicle.

### Path Length

It is the length of the curve joining the initial and final positions along which the particles has actually moved.

### Speed

The time rate of change of position of the object in any direction is called speed of  the object..

It is a scalar quantity, Its SI unit is m/s and its dimensional formula is [M0LT-1].For a moving body ,speed is always positive and can never be negative and zero.

#### Type Of  Speed

##### Uniform Speed

If an object covers equal distances in equal intervals of time, then its speed is called uniform speed or constant speed.

##### Non-uniform Speed

If an object covers unequal distances in equal intervals of time, then its speed is called non-uniform speed or variable speed.

##### Average Speed

The ratio of the total distance travelled by the object to the total time taken is called average speed of the object.

example :-

If a particles travels distance S1 + S2 + S3 +……..  with times t1 +t2 + t3 +……… then,

##### Instantaneous Speed

The speed of a particle at any instant of time is known as its instantaneous speed.

### Displacement

When a body moves from one position to another, the shortest distance i.e., straight line between the initial position and final position of the body along with direction is known as displacement. It is a vector quantity directed from initial position to final position. Its SI unit is metre.

• The magnitude of the displacement for a course of motion may be zero when the corresponding distance covered is not zero.
• Displacement of the object can be positive, negative or zero.
• Displacement of a moving object can never be greater than the distance travelled by it.

Displacement s Distance ≤ Displacement

Displacement / Distance  ≤ 1

i.e., the ratio of displacement and distance is always less than or equal to 1.

### Velocity

The time rate of change of displacement of a body is called its velocity. It is a vector quantity.

The SI unit of velocity is m/s and its dimensional formula is [ M0LT-1] .

• Velocity of an object can be changed by changing the object’s speed or direction of motion or both.
• The velocity of an object is taken to be positive if the object is moving towards the right of the origin and is taken to be negative if the object is moving towards the tent of the origin.
•  For an object in a time interval (1)

| Velocity| ≤ speed

i.e., the magnitude of velocity of an object is always equal to or less than its speed.

#### Types of Velocity

There are four types of velocity

(i) Uniform Velocity or Constant Velocity  If an object covers equal displacement in equal intervals of time, then it is said to be moving with a uniform velocity or constant velocity.

(ii) Non-uniform or Variable Velocity If an object covers unequal displacement in  equal intervals of time, then it is said to be moving with a non-uniform or variable velocity.

(iii) Average Velocity The ratio of the total displacement to the total time taken is called average velocity.

If Velocity Of the object changes at a uniform rate , them

(iv) Instantaneous Velocity The velocity of a particle at any instant of time is known as its instantaneous velocity. Its unit is m/s.  Speed and velocity have the same units i.e., m/s.

• If a body is moving in a single straight line, then the magnitude of its speed and velocity will  be equal.

### Relative Velocity

The relative velocity of one object with respect to another is the velocity with which one object moves with respect to another object. Hence, relative velocity is defined as the time rate of change of relative position of one object with respect to another.

If two objects a and b are moving with velocities Va and Vb  respectively then,

Relative velocity Vab = Va-Vb (if objects are moving in same direction)

Vab = Va+Vb (if objects are moving in opposite directions)

### Acceleration

The time rate of change of velocity of a body is called acceleration. It is a vector quantity, denoted by a and its SI unit is m/s2.

If in a given time intervalt the velocity of a body changes from u to v, then acceleration a is expressed as

When the velocity of a body increases with time, acceleration is positive and when the velocity of a body decreases with time (i.e., u>V), then acceleration becomes negative. Negative acceleration is also called deceleration or retardation.

#### Types of Acceleration

There are four types of acceleration

(i) Uniform Acceleration or Constant Acceleration If the velocity changes uniformly  at equal intervals of time, then acceleration is said to be uniform acceleration.

(ii) Non-uniform Acceleration or Variable Acceleration If the velocity of the particle does not change equally in equal intervals of time, then the acceleration is said to be non-uniform acceleration.

(ii) Average Acceleration When an object is moving with a variable acceleration, then the average acceleration of the object for the given motion is defined as the ratio of the total change in velocity of the object during motion to the total time.

• The average acceleration can be positive or negative depending upon the sign of change of velocity. It is zero if the change in velocity of the object in the given interval of time is zero.

(iv) Instantaneous Acceleration The acceleration of the object at a given instant of time or at a given point during the motion, is called its instantaneous acceleration.

## Uniform and Non -Uniform Motion

An object covers equal distances in equal intervals of time, it is said to be in uniform motion. e.g., a car moving along a straight line path such that it covers equal distances in equal intervals of time, then it is said to be in uniform motion.

On the other hand, if an object covers unequal distances in equal intervals of time, it is said to be in non-uniform motion, e.g., when a car is moving on a crowded street or a person is jogging in a park, these are said to be in non-uniform motion.

• The direction of motion changes at every point of motion in uniform circular motion. This De direction is given by that of a tangent drawn at that point.
• For uniform motion along a straight line in given direction, the magnitude of the displacement is equal to the actual distance covered by the object.
• No force is required for an object to be in uniform motion.
• The velocity in uniform motion does not depend upon the time interval.

## Equation Of Motion Class 9

When a body is moving along a straight line with uniform acceleration, we can establish the relation between velocity of the body, acceleration of the body and the distance travelled by the body in a particular time interval by a set of equations. These equations are known as equations of motion.

The three equations of motion on a straight line are

1. V = ut + at

2. S = ut + 1/2 at2

3. V2 –U2 = 2as

where u is the initial velocity of the body, a is the uniform acceleration of the body, v is the final velocity of the body after t second and s is the distance travelled in this time. Distance travelled in nth second given

Sn = u + ½ a(2n-1)

• Where, sn = distance covered by a body in nth second.

## Freely Falling Objects

The objects falling towards the earth under the gravitational force alone, are called freely falling objects and such fall is called free fall.

Whenever an object falls towards the earth, an acceleration is involved, this acceleration is due to the earth’s gravitational pull and is called acceleration due to gravity. The value of acceleration due to gravity near the earth surface is 9.8 m/s2

Though the value of g is independent of freely falling mass, a feather falls much slowly than a coin when released from a height. This is due to the resistance offered by air to the falling mass. If both the bodies were released at the same time in vacuum, they would reach the earth surface within the same duration of time.

The three equations of free fall of an object near the surface of the earth are

•  v = u + gt
• h= ut + ½ gt2
• v2 = u2+ 2gh

where h is the height from which the object falls, t is the time of fall, u is the initial velocity-and v is the final velocity when the body accelerates at g.

• The only difference between the equations of motion for object moving in straight line is that in place of acceleration a, we take acceleration due to gravity g.

### Cases of Free Fall

• If an object falls vertically downward then acceleration due to gravity is taken as positive (since its velocity increases while falling).
• If an object is thrown vertically upward then acceleration due to gravity is taken as negative (since its velocity decreases as it moves upward).
• If an object is dropped freely from a height, its initial velocity u is zero.
• If an object is thrown vertically upwards, its final velocity v becomes zero.
• Time taken by an object to fall from a height is same as that taken by it to rise the same heignt.

## Motion in a Plane

If an object is in the motion such that its position at any time can be given with reference axes (two mutually perpendicular lines passing through the origin) then the motion of object is said to be motion in a plane. Projectile motion, circular motion, etc are the examples of this motion.

## Projectile Motion Class 11

When an object is thrown obliquely near the earth’s surface, HAY its motion on a parabolic path is known as projectile motion and path followed by the object is called trajectory.

Projectile motion can be considered as combination of two independent onedimensional motion i.e., motion along a straight line; one along horizontal direction with constant velocity and the other along vertical direction under gravity effects.

• The motion of bullet fired through the firing tank shows the projectile motion.
• The motion of a rocket after burn out.
• The motion of a bomb dropped from an aeroplane.
• The motion of a ball thrown in a horizontal direction.
• The motion of a ball after hitting the bat, etc.

SSC CGL Salary