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NEET NEET SOLVED PAPER 2016 Phase-II

  • 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 \[{{X}_{p}}(t)=at+b{{t}^{2}}and\,{{X}_{Q}}(t)=ft-{{t}^{2}}\]. At what time do the cars have the same velocity?

    A)  \[\frac{a-f}{1+b}\]                   

    B)  \[\frac{a+f}{2(b-1)}\]

    C)  \[\frac{a+f}{2(1+b)}\]             

    D)  \[\frac{f-a}{2(1+b)}\]

    Correct Answer: D

    Solution :

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


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