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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 33

  • question_answer
    Two particles start moving from the same point along the same straight line. The first moves with a constant velocity v and the second with constant acceleration a. During the time that elapses before the second catches the first, the greatest distance between the particle is

    A) \[\frac{{{v}^{2}}}{a}\]           

    B)                    \[\frac{{{v}^{2}}}{2a}\]

    C) \[\frac{2{{v}^{2}}}{a}\]                     

    D)        \[\frac{{{v}^{2}}}{4a}\]

    Correct Answer: B

    Solution :

    [b] Let x be the distance between the particles after t seconds. Then \[x=vt-\frac{1}{2}a{{t}^{2}}\]                        ...(1) For x to be maximum,             \[\frac{dx}{dt}=0\] or         \[v-at=0\] or         \[t=\frac{v}{a}\] Substituting this value in (1), we get \[x=v\left( \frac{v}{a} \right)-\frac{1}{2}a{{\left( \frac{v}{a} \right)}^{2}}\] or         \[x=\frac{{{v}^{2}}}{2a}\]


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