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CMC Medical CMC-Medical Ludhiana Solved Paper-2012

  • question_answer
    A car A travelling on a straight road with uniform speed of 60\[km{{h}^{-1}}\] is followed by another car B moving at a speed of 70\[km{{h}^{-1}}\]. If the distance between the two cars is 2.5 km and the car B starts deceleration at the rate of 20\[km{{h}^{-1}}\], then after how much time will B catches A?

    A)  \[\frac{1}{8}h\]                                               

    B)  \[\frac{1}{4}h\]

    C)  \[\frac{1}{2}h\]                                               

    D)  \[1\,h\]

    Correct Answer: C

    Solution :

                    Let car B catches car A after t sec, then Distance travelled by A in t sec = Distance travelled by B in t sec \[\Rightarrow \]               \[60\,t+2.5=70\,t-\frac{1}{2}\times 20\,{{t}^{2}}\] \[\Rightarrow \]               \[10\,{{t}^{2}}-10\,t+2.5=0\] \[\Rightarrow \]               \[{{t}^{2}}-t+0.25=0\] or            \[t=\frac{1\pm \sqrt{1-4\times (0.25)}}{2}=\frac{1}{2}h\]


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