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NEET Sample Paper NEET Sample Test Paper-74

  • question_answer
    Displacement x of a particle moving in one dimension is related to time t by the equation\[\operatorname{t} =\sqrt{x} +2\]. The displacement of the particle when its velocity is zero, is (Here x is in metre and t in second)

    A)  4                                

    B)  2

    C)  1                                

    D)  0

    Correct Answer: D

    Solution :

    \[t=\sqrt{x}+2\] \[\sqrt{x}=t-2\] \[\operatorname{x}= {{\left( t - 2 \right)}^{2}}\]             (Squaring both sides) \[\operatorname{x}= {{t}^{2}}+4-4t\]                                      ? (i) Now velocity, \[v=\frac{dx}{dt}=\frac{d}{dt}({{t}^{2}}+4-4t)=2\,t-4\] \[v=0\,\,\Rightarrow \,\,2t\,-4=0\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,t=2\,\,s\] Putting \[r = 2\,\,s\] in                                         ... (ii) \[\operatorname{x}=4+ 4-8=0\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\operatorname{Displacement} = 0\]


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