RAJASTHAN ­ PET Rajasthan PET Solved Paper-2012

  • question_answer An electron starting from rest has a velocity\[v\] that increases linearly with time t as\[v=kt,\] where\[k=2\text{ }m{{s}^{-2}}\]. The distance covered by electron in first 3 s is

    A)  9m          

    B)  11 m

    C)  33m         

    D)  40m

    Correct Answer: A

    Solution :

     Given,         \[v=kt\] Also            \[k=2m{{s}^{-2}}\] \[\therefore \] \[v=2t\] or           \[\frac{dx}{dt}=2t\] On integration of both sides \[x={{t}^{2}}+c\] When,\[t=0,\]then \[x=0\] \[\therefore \] \[0={{(0)}^{2}}+c\] \[\Rightarrow \] \[c=0\] So, we get \[x={{t}^{2}}\] When       \[t=3~\] \[\Rightarrow \] \[x={{(3)}^{2}}=9m\]

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