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A particle moves according to the eqn a=-kv where a is acceleration and v is the velocity and k is a constant. If initial speed is V0 find the speed at any instant

  • physics -

    dv/dt = -kv

    dv/v = - k dt

    ln v = - k t + c

    e^ln v = v = e^(-kt +c) = e^c e^(-kt)

    when t = 0, v = Vo
    Vo = e^c e^0 = e^c
    so
    v = Vo e^-kt

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