Question

Which of the following is the correct equation for kinetic energy?

KE = 1/2mv^2
KE = mgh
KE = Fd
KE = mv

Answer 1

• 
  `{\boxed{\sf{\red{K.E = (1)/(2) mv^(2)}}}}`

Step-by-step explanation:

`{\underline{\underline{\bf{\orange{What \: is \: Kinetic\: Energy\:?}}}}}`

• The energy possessed by a body by virtue of its motion.

`{\underline{\underline{\bf{\green{Formula\:Derivation\::-}}}}}`

`\star\:\sf{Consider,}`

• Body of mass 'm' is moving with a velocity 'v'.
• A uniform force 'F' opposes the motion of a body and brings it to rest after a displacement 's'

`:\implies\:\:\sf{v^(2) -u^(3) = 2a}`

`:\implies\:\:\sf{0-v^(2) = 2as}`

`:\implies\:\:\sf{-v^(2)=2as}`

`:\implies\:\:\sf{a = (-v^(2))/(2s)}`

The opposing force on the body,

• F = ma = -mv²/2s

By Newton's 3rd law, the force applied by the body :-

`:\implies\:\:\sf{-F = -\bigg( -(mv^2)/(2s)\bigg) = (mv^2)/(2s)}`

`{\boxed{\bf{W = Force * Displacement}}}`

`:\implies\:\:\sf{W = F * S}`

`:\implies\:\:\sf{W = (mv^2)/(2s)* s = (1)/(2)mv^2}`

• We know that, Work done will be stored as kinetic energy in the body.

`\star\:\:{\underline{\boxed{\sf{\red{K.E = (1)/(2)mv^(2)}}}}}`

Answer 2

`\boxed{KE=(1)/(2)mv^2}`

Hope this helps.

r3t40