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Math Help - Derivatives: Velocity + Acceleration

  1. #1
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    Derivatives: Velocity + Acceleration

    The equation of motion of a particle, where s is in meters and t is in seconds, is given by the equation below.

    s = 5t^3 - 4t

    i know that

    v(t) = 15t^2 - 4
    and
    a(t) = 30t

    The question is "Find the acceleration when the velocity is 0. (Round the answer to one decimal place.)"

    I feel dumb asking this cause it seems like an easy problem, but i have no clue what the answer is.
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  2. #2
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    Quote Originally Posted by break View Post
    The equation of motion of a particle, where s is in meters and t is in seconds, is given by the equation below.

    s = 5t^3 - 4t

    i know that

    v(t) = 15t^2 - 4
    and
    a(t) = 30t

    The question is "Find the acceleration when the velocity is 0. (Round the answer to one decimal place.)"

    I feel dumb asking this cause it seems like an easy problem, but i have no clue what the answer is.
    Just set the velocity equal to zero and solve the quadratic for t.

    15t^2-4=0

    Just solve that equation for t, and then plug that into a(t) to obtain the acceleration.

    15t^2=4

    t= \frac{2}{\sqrt{15}}

    It's conventional to rationalize the denominator. So t could be written as \frac{2\sqrt{15}}{15}

    a(\frac{2\sqrt{15}}{15})=30(\frac{2\sqrt{15}}{15})  =4\sqrt{15}
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