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calculus

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a key is dropped from a height of 30 m , If its distance from the ground at t seconds after the release is given by the position function d (t) = 30-5t², find
a.its height velocity and acceleration after 1 second.
b. the time it reached the ground.
c. its position after 1 second

  • calculus - ,

    If d(t) = 30 - 5t^2 m, then the velocity is
    v(t) = -10t m/sec , and the acceleration is
    a(t) = -10 m/sec^2

    (each is the derivative of the previous function)

    a) when t = 1
    distance = 30 - 5(1^2) = 25 m
    velocity = -10(1) = -10 m/s
    acceleration = -10 m/s^2

    b) when it reaches the ground, d(t) = 0, so
    0 = 30 - 5t^2
    t^2 = 6
    t = √6 or appr. 2.4 seconds

    c) 25 m above the ground , already answered in a)

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