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Work and Energy - Kinetic Energy

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  • Expression for kinetic energy 

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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= v2 - u2 =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`

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