Question

prove that S = ut +1/2+ at2​

Answer 1

Correction in the question : S = ut + 1 / 2 at^2.

Answer:

S = ut + 1 / 2 at^2 .

Explanation:

This the second equation of motion and here acceleration is considered to be uniform.

Consider a body motion with uniform acceleration, having an initial velocity u and final velocity v. And S be the displacement covered with the change of velocities.

We know, average velocity of two two velocities = ( u + v ) / 2.

Here,

= > Average velocity = ( v + u ) / 2

= > S / t = ( v + u ) / 2

= > 2S = ( v + u )t

= > 2S = { ( at + u ) + u }t { v = u + at }

= > 2S = ( at + u + u )t

= > 2S = ( 2u + at )t

= > S = ( 2u + at )t / 2'

= > S = at + 1 / 2 at^2 .

Hence, S = at + 1 / 2 at^2.

Answer 2

refer to attachment

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