math and physics

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i just want to know form where i got on this formula the 4.9t² on this formula s=4.9t²+Vot+h because the book only say that a physics theory shows that when an object is thrown upward with an initial velocity Vo, its approximate height is given by that quadratic function

i will appreciate if you can explain me that because i have a math problem that uses that equation but i don't know from wheres that 4.9t²

  • math and physics -

    It comes from calculus, and I assume you do not know that.

    Newton found the velocity of a falling object was proportional to the time it fell.

    vincreased= constant*time

    but the constant we now call g, 9.8m/s^2, which comes from his universal gravitational equation.
    From this, we get
    Vfinal=vinitial+ g*time

    Now the distance something falls is the average velocity, times time.
    distance=(vfinal+vinitial)/2 * time
    d=(1/2 (vinital+ g*time + vinitial)*time
    = 1/2 (2vinitial*time + g*time^2)
    = vinitial*time + 1/2 g*time^2
    of course, 1/2 g = 4.9 m/s^2

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