Derive equation of uniform accelerated motion.

Explanation

1) Let 'u' be the velocity at the time t = 0 and 'v' be the velocity at the time 't' and let 's' be the displacement covered by the body during time 't' as shown in figure.
2) From the definition of uniform acceleration,
`a=(v-u)/t`
`rArrat=v-u`
`rArrv=u+at" "....(1)`
Since the acceleration of the body is constant,
Average velocity = `(v+u)/2`
But we known, average velocity = `("Displacement")/("Time")=s/t`
`therefores/t=(v+u)/2" "....(2)`
Substitute v = u + at in (2)
`s/t=(u+at+u)/2`
`s/t=(2u+at)/2`
`s/t=u+1/2at`
`s=ut+1/2at^(2)" "......(3)`
From (1), we know that v = u + at
`rArrt=(v-u)/a`
Substitute `t=(v-u)/a` in (2)
(2) `rArrs=(t(v+u))/2`
`rArrs=((v-u)(v+u))/(2a)`
`rArrs=(v^(2)-u^(2))/(2a)`
`rArrv^(2)-u^(2)=2as" ".....(4)` `therefore` Equations of uniform acceleration motion are
v = u + at
`s=ut+1/2at^(2)`
`v^(2)-u^(2)=2as`