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Math Help - By what factor does its speed increase?

  1. #1
    Member looi76's Avatar
    Joined
    Jan 2008
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    185

    By what factor does its speed increase?

    Question:
    The kinetic energy of a particle is increased by a factor of 4.
    By what factor does its speed increase?

    Attempt:
    \mbox{Kinetic Energy} = \frac{1}{2}mv^2
    So, the particle is the mass

    1 = \frac{1}{2}mv^2

    1 = \frac{1}{2}(4)v^2

    2 = 4 \times v^2

    \frac{2}{4} = v^2

    0.5 = v^2

    v = \sqrt{0.5}
    v = 0.707

    Where did I go wrong?I think all the steps are wrong right?
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  2. #2
    Super Member wingless's Avatar
    Joined
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    Istanbul
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    E_1 = \frac{1}{2}m (v_1)^2

    E_2 = \frac{1}{2}m (v_2)^2

    E_2  = 4E_1

    \frac{1}{2}m (v_2)^2 = 4\frac{1}{2}m (v_1)^2

    (v_2)^2 = 4 (v_1)^2

    v_2 = 2 v_1
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