The position of a particle is r⃗ (t)=(3.0t2iˆ+5.0jˆ−6.0tkˆ)m. (a) Determine its velocity and acceleration as functions of time. (b) What are

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The position of a particle is r⃗ (t)=(3.0t2iˆ+5.0jˆ−6.0tkˆ)m. (a) Determine its velocity and acceleration as functions of time. (b) What are its velocity and acceleration at time t = 0?

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Bơ 5 years 2021-07-23T05:43:03+00:00 1 Answers 135 views 0

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  1. dangkhoa
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    2021-07-23T05:44:42+00:00
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    Explanation:

    It is given that,

    The position of a particle is given by :

    r(t)=(3t^2i+5j-6tk)\ m

    (a) Velocity of a particle is given by :

    v=\dfrac{dr(t)}{dt}

    Putting values,

    v=\dfrac{d}{dt}(3t^2+5-6t)\\\\v=(6ti-6k)\ m/s

    The acceleration of the particle is given by :

    a=\dfrac{dv}{dt}\\\\a=\dfrac{d}{dt}(6t-6)\\\\a=6i\ m/s^2

    (b) At t = 0,

    Velocity, v = 6k m/s

    Acceleration, a = 6i m/s²

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