Question

Derive Newton's Third equation of motion with algebraic method

Answer 1

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Newton's Third equation of motion

✒ We know that

✒ v = u + at

✒ Squaring both sides

✒ v² = ( u + at )²

✒ v² = u² + 2uat + a²t²

✒ v² = u² + 2a ( ut + 1/2 at² )

✒ From second equation of motion we know that ( ut +1/2 at² ) = s

✒ v² = u² +2as

Third equation of motion

✏ v² = u² + 2as

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Answer 2

Newton's third law of motion :- according to " sir issac NEWTON", Action and reaction are of equal magnitude and directed in opposite direction.

It means if you apply force on a body then body must apply force on you.

Let you apply force on a body ' Fab'
Then according to NEWTON's 3rd law body must apply force on you 'Fba'.

Where ,
|Fab| = |Fba|
and Fab = - Fab

Derrivation of 3rd equation , We know, V = u + at , S = ut + 1/2at^2 -------------(1) Where v is the final velocity u is the initial velocity a is acceleration of body S is displacement covered by body and t is the time taken by body V = u + at Take square both sides, V^2 = u^2 + a^2t^2 + 2uat = u^2 + 2a{ 1/2at^2 + ut } Put equation (1) V^2 = u^2 + 2aS Hence, V^2 = u^2 + 2aS