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NCERT Revision notes for class 9 Physics Motion

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What is motion?

An object changing its position with respect to change in time is called motion.

Example:  A car moving on the road is said to be in motion.

Types of motion:

There are several types of motions:

  1. Rectilinear motion
  2. Circular motion
  3. Rotational motion
  4. Periodic motion

The motion along straight line is called rectilinear motion.

What is Uniform motion and non-uniform motion?

An object that covers equal distances in equal amount of time is called uniform motion.

An object that covers unequal distances in equal amount of time is called non-uniform motion.

What is speed?

The distance travelled by an object in unit time is called speed. The SI (Standard identity) unit of speed is m s-1 or m/s (metre per second). The formula of speed is:

Speed = distance / time

Formula for Average speed:

Average speed = total distance travelled / total time taken

Or

vav = s / t

Here, vav = average speed

s = total distance travelled

t = total time taken

What is velocity?

Velocity is the speed in the definite direction. The SI unit of velocity is m s-1 or m/s. The formula velocity is:

Velocity = displacement / time

Formula for average velocity

Average velocity =( initial velocity + final velocity) / 2  

Rate of change of velocity

Acceleration is defined as the rate of change of velocity, which means change in the velocity of an object per unit time.

Acceleration = change in velocity / time taken

Or

a = (v  - u) / 2

Here, a = acceleration

v = final velocity

u = initial velocity

Graphical representation of equations of motion

  1. v = u + at
  2. s = ut + ½ at2
  3. 2as = v2 – u2

The following graph will be used to derive all the above equations of motion

Equation for velocity-time relation (v = u + at)

chapter_motion_derivation_digram

Let the initial velocity of an object be u. Its velocity was increased to v with uniform acceleration a in time t.

The acceleration of an object is:

a = change in velocity / time taken

=> a = v – u / t

=> at = v – u

=> at + u = v

Or

=> v = u + at

Equation for position time relation (s = ut + ½ at2) :

chapter_motion_derivation_digram

Let an object travelled total distance s with uniform acceleration a in time t.

The distance travelled by an object is:

Distance = velocity x time

=> s = average velocity x time

=> s = (intial velocity + final velocity) / 2  x  time

=> s = (u + v) / 2 x t

=> s = [u + (u + at) /2 ] x t  [from I equation of motion, we have v = u + at]

=> s = [(u + u + at) / 2] x t

=> s = (2u + at) /2 x t

=> s = u + at / 2 x t

=> s = ut + ½ at2

Equation for position velocity relation (2as = v2 – u2)

chapter_motion_derivation_digram

Let the object travelled to total distance s with uniform acceleration a in time t.

The distance travelled by an object = the area of OABC

So, distance = area of trapezium OABC

=> s = ½ (sum of || sides) x height

=> s = ½ (OA + OB) X OC

=> s = ½ (u + v) x t

=> s = ½ (u + v) x (v – u)/a [From 1st equation of motion we have, t = v-u/a]

=> s = ½ (v2 – u2) / a

=> s = 1/2a (v2- u2)

=> 2as = v2 – u2

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