Question

Derive all the kinematic equations below..
$v = u + at$
$s = ut + \frac{1}{2} a {t}^{2}$
${v}^{2} = {u}^{2} + 2as$

Answer 1

1) (v-u)/t=a
v-u=at
v=at+u
v=u+at

2) v= (v+u)/2 v=average velocity
and s=(v+u)/2 ×2 ........... 1

s=((u+u+at)×t)/2 ............ v = u+ at
s=2ut+at^2
s=ut +1/2at^2

3) v=u+at
at=v-u
t=(v-u)/a .......1
s=ut+1/2×at^2 ( from 1)
s= (u(v-u))/a+1/2 ×a((v-u)÷a)^2
s=(uv-u^2)/a + (v^2+u^2-2uv)/2a
s=(2uv-2u^2+v^2+u^2-2uv)/2a
2as=v^2-u^2
v^2=u^2+2as