RAJASTHAN ­ PET Rajasthan PET Solved Paper-2006

  • question_answer
    The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity\[{{v}_{0}}\]. The distance travelled by the particle in time t will be

    A)  \[{{v}_{0}}t+\frac{1}{3}b{{t}^{2}}\]

    B)  \[{{v}_{0}}t-\frac{1}{3}b{{t}^{2}}\]

    C)  \[{{v}_{0}}t+\frac{1}{6}b{{t}^{3}}\]

    D)  \[{{v}_{0}}t+\frac{1}{2}b{{t}^{3}}\]

    Correct Answer: D

    Solution :

     \[\frac{{{d}^{2}}x}{d{{t}^{2}}}=bt\] The distance covered in time t by the particle \[s={{v}_{0}}t+\frac{1}{2}bt.{{t}^{2}}\] \[={{v}_{0}}t+\frac{1}{2}b{{t}^{3}}\]


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