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Derive the equation for kinetic energy

  1. Feb 24, 2015 #1

    Suraj M

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    question:
    I came across a question which said: Derive the equation for kinetic energy of a body of mass m and velocity v.
    What do they mean?
    Attempt:
    I actually just wrote that by work energy theorem diff. in KE = work done
    so Fx = KE
    $$ max = m \frac {v²-u²}{2x} x = ½mv² - ½mu² $$
    each of these terms represents a quantity called KE so this is the formula.
    Is this right?? Because i seriously doubt it.
     
  2. jcsd
  3. Feb 24, 2015 #2

    PeroK

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    That assumes constant acceleration. What if acceleration isn't constant?
     
  4. Feb 24, 2015 #3

    Suraj M

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    Then i would do this:
    $$ Fdx = dKE$$
    $$ ma.dx = m. \frac{dv}{dt}dx = m v dv$$
    $$mvdv = dKE$$
    $$ m~₀∫^x vdv = ΔKE$$
    $$ \frac{m(v^2 - u^2)}{2} = ΔKE $$
     
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