A particle moves along the x-axis so that at any time t≥0 its position is given by x(t)=12(a−t)2, where a is a positive constant. For what v

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A particle moves along the x-axis so that at any time t≥0 its position is given by x(t)=12(a−t)2, where a is a positive constant. For what values of t is the particle moving to the right? The particle is moving to the right only if 0

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Mộc Miên 3 years 2021-08-13T13:38:17+00:00 1 Answers 172 views 0

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  1. Eirian
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    2021-08-13T13:39:28+00:00
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    Answer:

    The particle moves to the right when 0 ≤ t < a

    Explanation:

    Since at any time t≥0 its position is given by x(t) = 12(a−t)², the particle moves to the right if x(t) > 0

    So,  x(t) > 0 ⇒ 12(a−t)² > 0 ⇒ (a−t)² > 0

    So, (a−t)² > 0

    taking square-root of both sides, we have

    √(a−t)² > √0

    ⇒ (a−t) > 0

    ⇒ a > t

    Since t ≥ 0 ⇒ a > t ≥ 0 ⇒ 0 ≤ t < a

    So, the particle moves to the right when 0 ≤ t < a

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