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MOTION Motion: A body is said to be in motion

when its position changes continuously with respect to a stationary object taken as a reference point.

Characteristic of Motion : A common

characteristic of all moving object are they change their position with respect to time.

Examples of motion:1. Swing

2. Merry go round

3. Pendulum of a clock

4. Hands of a watch

If a body moves fairly fast, then its movement can be observed easily. But if a body moves very slowly, then it become difficult to observe its movement immediately.

For example: A watch had three

hands i.e. a second’s, minute’s & hour’s. The speed of second’s is fast so, its motion can be observed. But the minute’s & hour’s hand is slow so, its motion cannot be observed.

Distance travelled:

The distance travelled b 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.

When a body moves from one point to another, the distance travelled refers to the actual length of the indirect path whereas displacement refers to the straight line path between the initial & the final positions.

Displacement: The shortest

distance between the initial position & the final position is known as its displacement.

It is a vector quantity.

Scalar quantity: A physical

quantity having only magnitude is known as a scalar quantity. A scalar quantity has no direction.

Vector quantity: A physical

quantity having only magnitude as well as direction is known as vector quantity.

The distance travelled by a moving body can't be zero but the final displacement of a moving body can be zero.

Uniform Motion:

A body has a uniform motion if it travels equal distances in equal intervals of time.

GRAPH OF UNIFORM MOTION

Non–Uniform Motion: A body

has a non–uniform motion if it travels equal distances in equal intervals. of time.

Non-uniform motion is also called accelerated motion.

Speed: Speed of a body is the distance

travelled by it per unit time. Formula for speed is:

Speed = Distance travelled Time taken

Where: v = speed s = distance travelled and t = time taken

Speed gives the idea how slow or fast the body is moving.

The SI unit of speed is meters per second.

The small values of speed are expressed in the unit of cm. per sec. To express high speed values we use the unit of km. per hr.

It is a scalar quantity because it has only magnitude not specified direction.

If we have to compare the speeds of a number of bodies, then we must express the speed of all of them in the same unit.

Average speed: The average sped of a

body is the total distance travelled by the total time taken to cover this distance.

Formula for Average speed is: Average speed = Total distance

travelled Total time taken

Where: v = average speed s = total distance travelled and t = total time taken

Speedometer: An instrument for

measuring speed of the moving vehicle.

Odometer: An instrument for

measuring distance travelled by the vehicle.

Uniform speed: A body has a

uniform speed if it travels equal distances in equal intervals of time.

Velocity: Velocity of a body is the

distance travelled by it per unit time in a given direction.Formula for Velocity is:

Velocity= Displacement Time taken

v = s tWhere: v = velocity s = displacement and t = time taken The SI unit of velocity is meter per

second. It is a vector quantity because is has

magnitude as well as direction. The direction of velocity is the same as

the direction of displacement of body.

Uniform velocity: A body has uniform

velocity if it travels in a specified direction in a straight line and moves over equal distances in equal intervals of time, no matter how small how these time intervals may be.

The velocity of a body can be changed in two ways:

(i) By changing the speed of the body, and

(ii) By keeping the speed constant but by changing the direction.

Speed and Velocity are not always equal in magnitude.

The magnitude of speed and velocity of a moving body is equal only if the body moves in a single straight line. If, however a body does not move in a single straight line, then the speed & velocity of the body is not equal.

The average speed of a moving can never be zero, but the average velocity of a moving body can be zero.

Acceleration: Acceleration of a

body is defined as the rate of change in velocity with time.

Formula for Acceleration is:

Acceleration = Final velocity – Initial velocity

Time taken a = v-u t

Where, a = acceleration of the body

v = final velocity of the body

u = initial velocity of the body

and t = time taken for the change in velocity The SI unit of acceleration is

“meter per second square.” Acceleration is a vector quantity

because it has magnitude as well as direction.

Uniform Acceleration: A body has

a uniform acceleration if the velocity changes at a uniform rate.

Example of Uniform Acceleration:i. The motion of a freely falling

body.ii. The motion of a bicycle going

down the slope of a road when the rider is not pedaling and wind is negligible.

iii. The motion of a ball rolling down an inclined plane.

The velocity-time graph of a body having uniformly accelerated motion is a straight line.

Non-Uniform Acceleration: A body

has a non-uniform acceleration if its velocity changes at a non-uniform rate.

Retardation: It is the negative of

acceleration.

GRAPH OF RETARDATION

GRAPH OF NON-UNIFORM ACCELERATION

If the velocity of a body increases the acceleration is positive and if the velocity decreases the acceleration is negative.

Formula for Retardation is: Retardation = Final velocity – Initial

velocity Time taken SI unit of retardation is meter per

second square. Retardation is actually

acceleration with negative sign.

Average Velocity: If the object is

changing at uniform rate, then average velocity is given by the arithmetic mean of initial velocity & final velocity for a given period of time. Formula for average velocity:

Average velocity = Initial velocity+ Final velocity

2

Derivation of Formula for Equation of Motion:

Equation 1- V = u+at

Consider a velocity time graph for a body moving under uniform acceleration ‘a’

Initial velocity u ≠ o In the v-t graph OA = DC = u (initial velocity) EO = BC = v (final velocity) AD = OC = t (time taken) BD = BC - DC = v - u

The slope of v-t graph gives the acceleration of the object.

acceleration ‘a’

a = BD = (v-u) AD t or v-u = at

or v = u+at

Equation 2- S= ut + ½ at^2

v-t graph Let the body travels distance ‘s’ in time

‘t’ under uniform acceleration ‘a’. Distance travelled (s) = area enclosed

under the velocity time graph. S = area of triangle ABD + area of rectangle OADC = ½ AD BD AO OC = AD = OC = t BD = EA =(v-u) AO = DC = u

OC = AD = t = ½ t (v-u) ut = ut ½ (v-u) t : Equation 1

We know that v u at v u at : Equation 2 Putting the value of v u at in Equation 1 We get, s ut + ½ (at) t s ut ½ at²

Equation 3- v² u² 2as

v-t graph Let the body travels distance ‘s’ in

time ‘t’ under uniform acceleration ‘a’.

Distance travelled (s) = area enclosed under the velocity time graph.

In the trapezium OABC Area ½ (sum of parallel side)

height ½ OC (OA CB) Distance travelled (s) s ½ t (u v) We know that v u at t v u a s ½ v u v u a

Circular Motion: When a body

moves in a circle, it is called circular motion.

When a body moves along a circular path, then its direction of motion keeps changing continuously.

Uniform Circular Motion: When a

body moves in circular path with uniform speed, its motion is called uniform circular motion.

s v² u² 2a

v² u² 2as

or v² u² 2as

The force is needed to produce circular motion.

Centripetal Force: The force which

is needed to make an object travel in a circular path is called centripetal force.

Example of Uniform Circular Motion:

i. Artificial satellite move in a circular motion around the earth.

ii. The moon moves around the earth.

iii. The earth moves around the sun.

iv. A athlete moving on a circular path with a constant speed.

v. The tip of a second’s hand of a watch.

To Calculate the Speed of a Body in Uniform Circular Motion:

v 2 22 r 7 t

SUMITTED TO

MR KHANKRIAL SIR

SUMITTED FROM

BISHMAY IX ‘C’