Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

Solve for v...?

p = 1 / [ √(1 - (v^2/c^2)) ]

Show your steps. Thank you! :)

3 Answers

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  • :-)
    Lv 4
    1 decade ago
    Favorite Answer

    p = 1 / [ √(1 - (v^2/c^2)) ]

    p [ √(1 - (v^2/c^2)) ] = 1

    squaring on both sides to get rid of the sq.root

    p^2 (1- (v^2/c^2)) = 1

    1 - (v^2/c^2) = 1 / p^2

    v^2/c^2 = 1 - (1/p^2)

    v^2 = c^2 (1 - (1/p^2))

    Apply sq.root on both sides to get v

    v = √ (c^2 (1 - (1/p^2)))

    v = c √ (1 - (1/p^2))

  • 1 decade ago

    p = 1 / [ √(1 - (v^2/c^2)) ]

    1/p = [ √(1 - (v^2/c^2)) ]

    (1/p)^2 = 1- (v^2/c^2)

    (1/p)^2 - 1 = -v^2/c^2

    c^2[(1/p)^2 - 1] = -v^2

    v^2 = [c^2 - c^2/p^2]

    v = +/- sqrt[c^2 - c^2/p^2]

  • p = 1 / [ √(1 - (v²/c²)) ]

    Square this equation,

    p² = 1 / (1-v²/c²)

    Cross multiply

    1-v²/c² = (1/p²)

    v²/c² = 1 - (1/p²)

    v² = c² [1 - (1/p²)]

    take square root

    v = c √[1 - (1/p²)]

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