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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 26

  • question_answer
    Two cars P and Q start from a point at the same time in a straight line and their positions are represented by \[{{\operatorname{x}}_{p}}(t)=at\,+b{{t}^{2}}\] and \[{{\operatorname{x}}_{Q}}(t)=ft\,-{{t}^{2}}\]. At what time do the cars have the same velocity

    A) \[\frac{f-a}{2(l+b)}\]

    B)                    \[\frac{a-1}{l\,+b}\]

    C) \[\frac{a+1}{2(b-1)}\]   

    D)        \[\frac{a+f}{2(l+b)}\]

    Correct Answer: A

    Solution :

    \[{{V}_{p}}=\frac{d{{x}_{p}}}{dt}=a+2bt\] and \[{{V}_{Q}}=\,\,\frac{d{{x}_{Q}}}{dt}=f-2t,\,\,\,Given,\,\,{{V}_{p}}={{V}_{Q}}\,\,\] \[\therefore \,\,\,a+2bt=f-2t\,\,\,\Rightarrow \,\,t=\frac{f-a}{2(b+1)}\]


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