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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Self Evaluation Test - Application of Derivatives

  • question_answer
    The velocity v of a particle at any instant t moving in a straight line is given by v = s + 1 where s metre is the distance travelled in t second. What is the time taken by the particle to cover a distance of 9m?

    A) 1 s

    B) \[(log\,\,10)s\]

    C) \[2\text{(}log\text{ }10)s\]

    D) \[10s\]

    Correct Answer: B

    Solution :

    [b] Given velocity is \[v=s+1\] Since, velocity \[=\frac{ds}{dt}\] \[\therefore \frac{ds}{dt}=s+1\Rightarrow \frac{ds}{s+1}=dt\] Integrate both side we get \[\log (s+1)=t\] At \[s=9\,\,m,\] \[t=\log (10)\] second


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