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Physics Linear Motion formulae Derivations!!

  • 15-06-2008 12:01am
    #1
    mike-gunners
    Closed Accounts Posts: 33 ✭


    1. v= u + at

    from the definition of acceleration, acceleration is the rate of change of velocity,

    therefore => a = (v-u)/t (v=final Velocity, u = initial velocity)

    => at = v-u
    => at + u = v
    => v = u + at*

    2. s = ut + 1/2 at^2

    Displacement = Average Velocity X time

    => s = ( u + v)/2 X t

    But V = u + at

    => s = ( u + u + at)/2 X t

    => s = (2u + at)/2 X t

    => s = (u + at/2 ) X t

    => s = ut + 1/2 at^2

    3. v^2 = U^2 + 2as

    Displacement = average velocity X ime

    => s = (u + v)/2 X t

    but t = (v-u)/a (rearranging v = u + at)

    => s = (u + v)/2 X (v-u)/a

    => s = (uv - u^2 + v^2 - uv)/2a ( multiplying out the brackets)

    => s = ( v^2 - u^2)/2a

    => 2as = v^2 - u^2

    => 2as + u^2 = v^2

    => v^2 = u^2 + 2as


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