Question

using velocity time graph prove that v2 - u2 = 2as

Answer 1

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Answer 2

Given that,

The equation is,

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

We need to prove this equation

Using diagram

Displacement covered during the time interval is

$t'-t=Area\ of\ ABtt'$

$Area\ of\ trapezium=Area\ of\ triangle\ ABA'+Area\ of\ rectangle\ AA't't$

$Area\ of\ trapezium=\dfrac{1}{2}\times\ sum\ of\ parallel\ sides\times\ perpendicular\ distance$

Put the value into the formula

$s=\dfrac{1}{2}(v+u)\times t$

Put the value of t from equation of motion

$s=\dfrac{1}{2}(v-u)\times\dfrac{v-u}{a}$

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

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

Hence, This is proved.