Question

i know that we use v²-u²/2a to derive formula...but what is wrong here? I should be getting mv²/2.
(u=0)​

Answer 1

Hey mate,

here's the correct formula:

Expression for Kinetic energy(Ek)-

Consider an object with mass m, moving with initial velocity u. Let a force F, act on it causing a displacement s, along the direction of force and accelaration. Let the object attain final velocity v.

We know

$F = m a --- 1 \\ By \: position \: velocity \: relation \\we \: have, \: V2 = u2 + 2as \\ </p><p>or\: s = v2 -u2 / 2a ------ 2 \\ The \: work \: done \: by \: the \: force \\ W = F x s ------ 3 \\ Substituting \: 1 \: and \: 2 \: in \: 3 \\ W = (ma) × (v2 - u2/2a) \\ W = m/2 (v2 - u2) \\ W = 1/2 mv2 - 1/2 mu2 ----- 4 \\ For \: an \: object \: to \: be \: at \:rest \: in \: the \: beggining, \\ u = 0 \\Therefore, \\ W = 1/2 m {v}^{2} \\ W = Ek ( Ek = kinetic\: energy) \\ Therefore, \: Ek = 1/2 m {v}^{2}$

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