An object attached to a horizontal spring is oscillating back and forth along a frictionless surface. The maximum speed of the object is 1.4

Question

An object attached to a horizontal spring is oscillating back and forth along a frictionless surface. The maximum speed of the object is 1.47 m/s, and its maximum acceleration is 6.24 m/s2. How much time elapses betwen an instant when the object’s speed is at a maximum and the next instant when its acceleration is at a maximum?

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Kim Cúc 2 months 2021-07-22T01:30:00+00:00 1 Answers 6 views 0

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    2021-07-22T01:31:31+00:00

    Answer:

    t = 0.37 seconds

    Explanation:

    t = (1/4)T

    Maximum acceleration is;

    a_max = Aω²

    In simple harmonic motion, we know that v_max = Aω

    Thus, a_max = v_max•ω

    ω = a_max/v_max

    We know that Period is given by;

    T = 2π/ω

    From initially, t = (1/4)T so, T = 4t

    Thus, 4t = 2π/(a_max/v_max)

    t = (2π/4)(v_max/a_max)

    We are given;

    Maximum velocity;v_max = 1.47 m/s

    Max acceleration;a_max =6.24 m/s²

    Thus,

    t = (2π/4)(1.47/6.24)

    t = 0.37 seconds

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