The position of a particle is given by the function x = \left(2t^3 – 6t^2 + 12\right) m, where t is in s. Question:At what time is the accel

Question

The position of a particle is given by the function x = \left(2t^3 – 6t^2 + 12\right) m, where t is in s. Question:At what time is the acceleration zero? (with working out)

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Vodka 4 years 2021-07-28T20:57:13+00:00 1 Answers 13 views 0

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  1. kiet
    0
    2021-07-28T20:59:03+00:00
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    Answer:

    t = 1sec

    Explanation:

    Given the position of a particle  expressed by the equation x = (2t^3 – 6t^2 + 12)m, where t is in seconds, the acceleration function can be gotten by taking the second derivative of the function with respect to t as shown;

    a = d/dt(dx/dt)

    First let us get dx/dt

    dx/dt = 3(2)t³⁻¹-2(6)t²⁻¹+0

    dx/dt = 6t²-12t

    a = d/dt(dx/dt)

    a = d/dx(6t²-12t)

    a = 2(6)t²⁻¹-12t¹⁻¹

    a = 12t – 12t⁰

    a = 12t-12

    If the acceleration is zero, then;

    12t-12 = 0

    add 12 to both sides

    12t-12+12 = 0+12

    12t = 12

    t = 12/12

    t = 1sec

    Hence the time when acceleration is zero is 1sec

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