Question

Define v^2=u^2+2as without graph

Answer 1

1st step:

velocity=distance/time traveled

$v = s \div t$

2nd step:

$acceleration = rate \: of \: Δv \div t$

$initial \: velocity \: = u$

$a = Δv \div t \\ a = (v - u) \div t \\ at = (v - u) \\ v = u + at \: - - - (eq.1)$

3rd step:

$average \: velocity = v + u \div 2 \\ apply \: v = s \div t \\ s = vt \\ subtitute \: the \: average \: velocity s =( (v + u) \div 2)t$

$average \: velocity =(v+u)/2 \: \\ \: apply \: v=s/t \\ s=vt \: \\ subtitute \: the \: average \: velocity \: \: s=[(v+u)/2]t$

SUBSTITUTE EQ.1

$s=[(at+u+u)/2]t \\ </p><p>s=[(at+2u)/2]t \: \\substitute \: s=[at/2+u]t \\ </p><p>s={at}^{2}/2+tu \: - - - - - - (2)$

4th step:

eq'n 1; (v=u+at) = (v=u+at)²

v²=(u+at)²⇔expand

v²=u²+2atu+a²t²⇔factor 2a

v²=u²+2a(tu+at²/2)⇔eq'n 2

v²=u²+2as

I HOPE THIS HELPS...

THANKS...PLEASE MAKE IT BRILLIANT