4.76 A car starts from rest on a curve of radius 120 m and accelerates tangentially at 1.0 m/s2 . Through what angle will the car have trave

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4.76 A car starts from rest on a curve of radius 120 m and accelerates tangentially at 1.0 m/s2 . Through what angle will the car have traveled when the magnitude of its total acceleration is 2.0 m/s2

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Gia Bảo 4 years 2021-07-28T21:30:10+00:00 1 Answers 99 views 0

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  1. Philomena
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    2021-07-28T21:32:06+00:00
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    Answer:

    The angle is 28.64°

    Explanation:

    Given:

    Radius of curve r = 120 m

    Tangential acceleration a_{t} = 1 \frac{m}{s^{2} }

    Total acceleration a = 2 \frac{m}{s^{2} }

    From equation total acceleration,

       a = \sqrt{a_{t}^{2}+ a_{c}^{2} }

    Find centripetal acceleration,

      a_{c} = \sqrt{a^{2}- a_{t} ^{2} }

      a_{c} = \sqrt{4-1 }

      a_{c} = 1.73 \frac{m}{s^{2} }

    From equation of centripetal acceleration,

      a_{c} = \frac{v^{2} }{r}

       v = \sqrt{a_{c} r }

       v = \sqrt{207.6}

       v = 14.41 \frac{m}{s}

    From the equation of kinematics,

       d = \frac{v^{2} }{2a_{t} }

       d = \frac{207.6}{2 \times 1.73}

       d = 60 m

    For finding the angle,

       d = r\theta

       \theta = \frac{d}{r}

       \theta = \frac{60}{120}

       \theta = 0.5  rad

       \theta = 28.64°

    Therefore, the angle is 28.64°

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