Prove the correctness of this equation s=vt + 1/2at ​

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Prove the correctness of this equation s=vt + 1/2at ​

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Thiên Di 5 years 2021-09-04T19:49:40+00:00 1 Answers 20 views 0

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  1. Adela
    0
    2021-09-04T19:51:26+00:00
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    Answer:

    The formula is dimensionally correct.

    Explanation:

    Given

    s = ut + \frac{1}{2}at^2

    Required

    Prove its correctness

    Write out the dimension of each:

    s = M^0LT^0 — displacement

    ut = M^0LT^{-1} * T — velocity * time

    \frac{1}{2}at^2 = M^0LT^{-2} * T^2 — acceleration * square of time

    The expression becomes:

    s = ut + \frac{1}{2}at^2

    M^0LT^0 = M^0LT^{-1} * T + M^0LT^{-2} * T^2

    Apply law of indices

    M^0LT^0 = M^0LT^{-1+1} + M^0LT^{-2+2}

    M^0LT^0 = M^0LT^{0} + M^0LT^{0}

    M^0LT^0 = M^0LT^{0}

    Both sides of the equation are equal

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