A particle moves along a straight line with the acceleration a = (12t – 3t ^ 1/2) feet / s ^ 2, where t is in seconds. Determine your speed

Question

A particle moves along a straight line with the acceleration a = (12t – 3t ^ 1/2) feet / s ^ 2, where t is in seconds. Determine your speed and position as a function of time. When t = 0, v = 0 and s = 15 feet.

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Mít Mít 5 months 2021-08-19T04:01:11+00:00 1 Answers 4 views 0

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    2021-08-19T04:02:13+00:00

    Answer:

    v = 6t² − 2t^³/₂

    s = 2t³ − ⅘t^⁵/₂ + 15

    Explanation:

    a = 12t − 3t^½

    Integrate to find velocity.

    v = ∫ a dt

    v = ∫ (12t − 3t^½) dt

    v = 6t² − 2t^³/₂ + C

    Use initial condition to find C.

    0 = 6(0)² − 2(0)^³/₂ + C

    C = 0

    v = 6t² − 2t^³/₂

    Integrate to find position.

    s = ∫ v dt

    s = ∫ (6t² − 2t^³/₂) dt

    s = 2t³ − ⅘t^⁵/₂ + C

    Use initial condition to find C.

    15 = 2(0)³ − ⅘(0)^⁵/₂ + C

    15 = C

    s = 2t³ − ⅘t^⁵/₂ + 15

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