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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Application in Mechanics and Rate Measurer

  • question_answer
    Moving along the x-axis are two points with \[x=10+6t;x=3+{{t}^{2}}.\]The speed with which they are reaching from each other at the time of encounter is (x is in cm and t is in seconds)                                       [MP PET 2003]

    A)            16 cm/sec

    B)            20 cm/sec

    C)            8 cm/sec

    D)            12 cm/sec

    Correct Answer: C

    Solution :

               Time of encounter \[10+6t=3+{{t}^{2}}\]                    Þ \[{{t}^{2}}-6t-7=0\], \[t=7\]sec.                    At \[t=7\sec \]., \[{{v}_{1}}=\frac{d}{dt}(10+6t)=6\,\]cm/sec                    At\[t=7\sec .\]  \[{{v}_{2}}=\frac{d}{dt}(3+{{t}^{2}})=2t=2\times 7=14\]cm/sec                    \Resultant velocity = \[{{v}_{2}}-{{v}_{1}}=14-6=8\,\]cm/sec


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