Derive the equation s=ut+1/2at^2 for position_time relation for an obj

1.	Derive the equation s=ut+1/2at^2 for position_time relation for an object travelling under uniform acceleration on straight path
Answer» Explanation: We know that DISPLACEMENT(s) = average velocity x TIME( t) But for the same time, average velocity = ( u + v) /2 => s = ( u + v )/2 x t Also, according to the 1st equation of motion, v = u + at substituting for v, we get: s = ( u + u + at) /2 x t => s = ( 2u + at) /2 x t => s =( 2ut + at^2 )/2 => s = ut + 1/2at^2 Hence PROVED.

Derive the equation s=ut+1/2at^2 for position_time relation for an object travelling under uniform acceleration on straight path

Answer»

Explanation:

We know that

DISPLACEMENT(s) = average velocity x TIME( t)

But for the same time,

average velocity = ( u + v) /2

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

Also, according to the 1st equation of motion,

v = u + at

substituting for v, we get:

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

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

=> s =( 2ut + at^2 )/2

=> s = ut + 1/2at^2

Hence PROVED.

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Derive the equation s=ut+1/2at^2 for position_time relation for an object travelling under uniform acceleration on straight path

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