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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Critical Thinking

  • question_answer
    The distance travelled s (in metre) by a particle in t seconds is given by, \[s={{t}^{3}}+2{{t}^{2}}+t.\]The speed of the particle after 1 second will be [UPSEAT 2003]

    A) 8 cm/sec

    B) 6 cm/sec

    C) 2 cm/sec

    D) None of these

    Correct Answer: A

    Solution :

    • \[s={{t}^{3}}+2{{t}^{2}}+t\]             
    • \[v=\frac{ds}{dt}=3{{t}^{2}}+4t+1\]           
    • Speed of the particle after 1 second           
    • \[{{v}_{(t=1)}}={{\left( \frac{ds}{dt} \right)}_{(t=1)}}=3\times {{1}^{2}}+4\times 1+1=8\,cm/sec.\]


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