Made BY :- SanchitClass 9th- C

Describing Motion • Motion :- Motion is the change in position

of a body with time.• Motion can be described in terms of the (i) distance moved or the (ii)displacement

(i)Distance moved is the actual length of the path travelled by a body.

(ii)Displacement is the length of the shortest path travelled by a body from initial position to it’s final position.

Example of the motion The average

speed of bullet train is

320km/hrs

A car is in

motion.

Motion of the Ball

Downward.

• i) Uniform motion :- If a body travels equal distances in equal intervals of time, it is said to be

in uniform motion.• ii) Non uniform motion :- If a

body travels unequal distances in equal intervals of time, it is

said to be in non uniform motion.

Uniform motion and Non uniform motion

Example

A movement of a asteroid and the bouncing of ball is the example of non uniform motion.

The movement of clock’s hand and movement of pendulum is the example of uniform motion

• Speed :- of a body is the distance travelled by the body in unit time.

Speed = Distance/Time • If a body travels a distance s in time t

then its speed v is v = s/t • The SI unit of speed is meter per second

m/s or ms -1 . Since speed has only magnitude it is a scalar quantity.

Example

The red car is at the speed of 30m/sAnd,

The gray car is at the speed of 40m/s

Average speed Average speed :- is the ratio of the total distance travelled to the total time taken.

Example Problems Q. A car travels 85km from point A to B , then 45km

from point B to C . The total time took was 1.3 hrs. What was the average speed of the Car?

Solution of the problem

Total distance=Distance covered i)A to B + ii)B to C85km + 45km= 130km

Total Time = 1.3 hrs Average speed = Total Distance Covered/Total time

=> 130/1.3 km/hrs=> 100km/hrs

The quantity which specifies both the direction of motion

and speed is velocity.• Velocity of a body is the

displacement of the body per unit time.

Velocity =Displacement/time taken

•Since velocity has both magnitude

and direction, it is a vector quantity.

Example

Speed with Direction is known

as Velocity

Average Velocity• Average velocity :- is the ratio of

the total displacement to the total time taken.

• Average velocity =Total Displacement/Total Time.

• Average velocity is also the mean of the initial velocity u and final velocity

v.• Average velocity= (initial velocity +

finial velocity)/2 or

(u+v)/2 • Speed and velocity have the same

units m/s or ms -1

Example ProblemQ. If a car changes its speed from 10m/s to

20m/s in just 5 sec. What is the average velocity of the car?

Sol. u = 10m/s time taken v = 20m/s = 5sec

Average velocity = (u + v)/2 Þ (20m/s + 10m/s)/2

Þ 30m/s/2 Þ 15m/s

The quantity which specifies changes in velocity is acceleration.

• Acceleration :- is the rate of change of velocity.

• Acceleration = (Final velocity – initial velocity) / 2

• If the velocity of a body changes from initial value u to final value v

in time t, then acceleration a is a = (v-u) /2

• The SI unit of acceleration is ms - 2

Example

Four different ways to accelerate a car.

Distance –Time Graph • Motion can be represented on the

distance time graph. • In the graph distance is taken on the y –

axis and time is taken on the x – axis.• The distance time graph for uniform

speed is a straight line.• This is because in uniform speed a

body travels equal distances in equal intervals of time.

Example

Uniform Motion

Derivation of three formula of motion

• Let a body is moving with initial velocity ‘u’ with uniform acceleration ‘a’ it’s velocity

become ‘v’ in time ‘t’ sec. In the meantime it covers the distance ‘s’

• The term would be in 1. Acceleration -> m/s2

2. Initial and final velocity -> m/s3. Time -> sec

4. Distance -> m

1st Equation of motion• Acceleration = (v – u)/t

a = (v - u)/tÞ at = v – uÞ u + at = v 1st

equation of

motion

2nd Equation of motion• Average velocity = (v + u)/2

• Distance Travelled = Av. Velocity + time s = (v + u)/2 x t

Put v = u + atÞ s = (u + at + u)/2 x t

Þ s = (2u+at)/2 x tÞ s = (2ut + at2) /2Þ s = ut + ½ at2 2nd

Equation of motion

3rd Equation of motion • We know that v = u + at

Þ v – u = atÞ (v - u)/a = t

• Put t = (v – u)/a in eq. s = ut + ½ at2

s = u{(v – u)/a} + ½a {(v-u)/2} 2

Þ s = (uv - u2)/a + ½a{(v2 + u2 -2uv)/a2}Þ s = (uv - u2)/a + ½(v2 + u2 -2uv)/aÞ s = (uv - u2)/a + (v2 + u2 -2uv)/2aÞ s = (2uv - 2u2 + v2 + u2 -2uv)/2a

Þ s = (v2 - u2 )/2aÞ 2as = v2 - u2

3rd Equation of motion

Circular motion • The motion of a body in a circular path is called

circular motion.• Uniform circular motion :- If a body

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

• Uniform circular motion is accelerated motion because in a circular motion a body continuously changes its direction.

• The circumference of a circle of radius r is given by 2лr. If a body takes time t to go once around the circular path, then the velocity v is given by

v = 2лr/2

Example