Question

List all the derivations of physics class 9th

Answer 1

1. v=u+at
we know, a = v-u/t
                at = v-u
                v = u+at
2. s=ut+1/2at^2
We know, s = Average v X t
Average v = (u+v)/2
.:  s = (u+v)/2 X t                 – eq.(1)
Again we know that:
v = u + at
substituting this value of “v” in eq.(1), we get

    s = (u+u+at)/2 x t
=>s = (2u+at)/2 X t
=>s = (2ut+at^2)/2
=>s = 2ut/2 + at^2/2

or s = ut +1/2 at^2

3. v^2 = u^2 +2as

We know that
     v = u + at
=> v-u = at
or t = (v-u)/a                         –   eq.(1)

Also we know that
   s = average v X t
.: s = [(v+u)/2] X [(v-u)/a]   –  (from above)
=> s = (v^2 – u^2)/2a

=>2as = v^2 – u^2

or v^2 = u^2 + 2as