Question

Derive the below equations of motion v=u+at v²-u²=2as​

Answer 1

Equations of Motion For Uniform Acceleration

It is described in terms of displacement, distance, velocity, acceleration, time and speed. ... The three equations are, v = u + at. v² = u² + 2as.

Answer 2

Answer:

this is the derivation of first and third equation of motion

Explanation:

equation 1 {v = u + at}

acceleration = v - u / t

at( transposition of t ) = v - u

thus the final equation at = v - u

equation 3

$v^{2} = u^{2} + 2as$ ( velocity position relation )

s/t ( displacement ) = v + u / 2

t = v - u /a  { equation 1  }

s = ( v + u / 2 ) + ( v - u ) / a ( replace t by equation 1 )

using identity 3 (a+b)(a-b)

s = $v^{2} -vu + vu-u ^{2}$/ 2a

s = $v^{2} - u^{2}$ / 2a ( vu gets cancelled because signs are opposite )

2as = $v^{2} - u^{2}$

if rearranged we get $v^{2} = u^{2} + 2as$