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You are here: Home / Class 9 / Motion / Equation of Motion by Graphical Method

Equation of Motion by Graphical Method

Last Updated on July 1, 2021 By Mrs Shilpi Nagpal 19 Comments

Question 1 What is meant by uniform circular motion?

Question 2 A body goes around the sun with constant speed in a circular orbit. Is the motion uniform or accelerated?

Question 3 A satellite goes around the earth in a circular orbit with constant speed. Is the motion uniform or accelerated?

Question 4 Give examples of circular motion?

Question 5 What is a centripetal force. Give example?

Question 6 A cyclist goes around a circular track once every 5 minute. If the radius of the circular track is 110 meters, calculate his speed?

Question 7 Derive first equation of motion by graphical method?

Question 8 Derive second equation of motion by graphical method?

Question 9 Derive third equation of motion by graphical method?

Contents

  • 1 Uniform Circular Motion
  • 2 Equation of Motion by Graphical Method
    • 2.1 (1) Derivation of v=u + at
    • 2.2 (2) Derivation of  S = ut +1/2 x at2
    • 2.3 (3) Derivation of v2  = u2  + 2as

Uniform 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 on changing continuously.

Since the velocity changes (due to continuous change in direction) therefore the motion along a circular path is said to be accelerated. When a body moves in a circular path with uniform speed its motion is called uniform circular motion. The velocity of the body moving in a circle with uniform speed is not uniform because the direction of motion is constantly changing.

For Example:

A stone tied to a thread is rotated in circular path with uniform speed in clockwise direction.

A → Speed is directed towards east.
B → Speed is directed towards south.

Since there is change in direction of speed, the velocity is not uniform.

The motion in a circle with constant speed is an example of accelerated motion.
The force which is needed to make an object travel in circular path is called centripetal force.

For Example :

(1) Movement of artificial satellite around earth .

(2) Motion of moon around earth.
(3) Motion of earth around sun.
(4) Tip of seconds hand of a watch.
(5) Athlete moving on a circular path.

The speed of a body moving along a circular path is given by:

                                      v=2nr/t

Equation of Motion by Graphical Method

Screen Shot 2016-05-30 at 8.55.52 am

(1) Derivation of v=u + at

Initial velocity u at A =OA
Velocity changes from A To B in time t(uniform acceleration a)
Final Velocity v=BC
BC=BD+DC
v=BD+AO
v=BD+u
Slope of velocity time graph is equal to acceleration a.
a= BD

a=BD/AD
a=BD/t
BD = at
v=u+at     

(2) Derivation of  S = ut +1/2 x at2

The distance travelled by the body is given by area of the space between velocity time graph AB and time axis OC , which is equal to area of figure OABC.
Distance travelled=Area of figure OABC
= Area of rectangle OADC + Area of triangle ABD
=(OA x OC) + 1/2 x AD x BD)
=(u x t) + (1/2 x t x at)
S = ut + 1/2 x at2            

(3) Derivation of v2  = u2  + 2as

The distance travelled by body in time t is given by area of figure OABC (which is a trapezium)

s = Area of trapezium OABC
s= Sum of parallel sides x height / 2
s= (OA+OB) x OC / 2
s=(u+v) x t /2

v=u + at
at = v – u
t= v-u /a

s= (u+v) x (v- u)/2a
2as = v2  – u2 

v2  = u2  + 2as

Filed Under: Motion, Class 9 Tagged With: centripetal force, example of centripetal force, motion, uniform circular motion, v2 = u2 + 2as, v=u +at

About Mrs Shilpi Nagpal

Author of this website, Mrs Shilpi Nagpal is MSc (Hons, Chemistry) and BSc (Hons, Chemistry) from Delhi University, B.Ed (I. P. University) and has many years of experience in teaching. She has started this educational website with the mindset of spreading Free Education to everyone.

Reader Interactions

Comments

  1. Neetu Singh says

    April 19, 2018 at 3:52 pm

    Easy

    Reply
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    September 26, 2018 at 8:30 pm

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    January 16, 2021 at 7:05 pm

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  15. Daksh Saraswat says

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  16. Vasanthakumar V says

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  17. Abchaka says

    September 28, 2021 at 6:27 am

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