#### description

- Expression for kinetic energy

#### notes

**Formula for Kinetic Energy:**

Work done → W = F x s ...(i)

due to force, the velocity changes to 'v', and the acceleration produced is 'a'

`therefore` relationship between v, u, a and s= v^{2} - u^{2} =2as

`therefore` `"s" = ("v"^2 - "u"^2)/"2a"` ...(ii)

F = ma ...(iii)

substitute (ii) and (iii) in (i) we get

W = F x s

`= "ma" xx ("v"^2 - "u"^2)/"2a"`

`"W" = 1/2 "m"("v"^2 - "u"^2)`

if u = 0, (object starts at rest)

`therefore` `"W" = 1/2"mv"^2`

Work done = Change in kinetic energy

`therefore` `"E"_"k" = 1/2"mv"^2`