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JEE Main & Advanced Mathematics Differential Equations Question Bank Application of differnetial equations

  • question_answer
    A particle moves in a straight line with a velocity given by \[\frac{dx}{dt}=x+1\](x is the distance described). The time taken by a particle to traverse a distance of 99 metre is

    A)                 \[{{\log }_{10}}e\]              

    B)                 \[2{{\log }_{e}}10\]

    C)                 \[2{{\log }_{10}}e\]            

    D)                 \[\frac{1}{2}{{\log }_{10}}e\]

    Correct Answer: B

    Solution :

                       \[\frac{dx}{dt}=x+1\] Þ \[\log (x+1)=t+c\]         Putting \[t=0,\ x=0\], we get \[\log 1=c\] Þ \[c=0\]                 \[\therefore t=\log (x+1)\].   For \[x=99,\ t={{\log }_{e}}100=2{{\log }_{e}}10\].


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