Question

what is the
diamensional answer of v²equal u²+2as​

Answer 1

So i am having a slight problem deriving this equation. there is a simple way which is v=u+at -> t = v-u/a s = (v+u)t/2 so s = (v+u)*(v-u)/2a 2as = (v+u)(v-u) 2as = v2-u2 v2=u2+2as but i am having trouble understanding this way V2=(u+at)2 V2=(u+at)(u+at) V2=u2+a2t2+2uat - i cant understand how you get from this to; V2=u2+2a(ut+0.5at2)

Reference https://www.physicsforums.com/threads/derive-v2-u2-2as.633623/

Answer 2

v^2 = u^2+2as

PROOF : V = u + at
squaring both sides,
v^2= (u+at)^2
v^2 = U^2 + 2uat + a^2t^2
v^2=u^2 + 2a(ut+ 1/2at^2)
v^2=u^2 + 2as
(because s=ut+1/2at^2)
This is by far the simplest derivation I’ve found. There are ofcourse another derivations, maybe you’d find this easy.
s = (v+u/2) x t —(1)

a=v-u/t
t=v-u/a—(2)

Using t=v-u/a in equation 1,

s = (v+u)(v-u)/2a
2as=(v+u)(v-u)
2as=v^2-u^2
v^2=u^2+2as

Obviously there are more derivations, but not to make it any longer, I’m only mentioning these two.

Hope it helps. You can ask if there are any doubts.