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9th Class Science Time and Motion Question Bank Motion

  • question_answer
    A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in the \[{{n}^{th}}\] second to distance covered in n seconds is

    A)  \[\frac{2}{n}-\frac{1}{{{n}^{2}}}\]             

    B)         \[\frac{1}{{{n}^{2}}}-\frac{1}{n}\]

    C)  \[\frac{2}{{{n}^{2}}}-\frac{1}{n}\]          

    D)         \[\frac{2}{n}-\frac{1}{{{n}^{2}}}\]

    Correct Answer: A

    Solution :

     We know, \[{{s}_{n}}=u+\frac{a}{2}(2n-1)=0+\frac{a}{2}(2n-1)\] Again,   \[s=ut+\frac{1}{z}a{{t}^{2}}\]             \[=0+\frac{1}{2}a{{n}^{2}}\]             \[[\because \,\,t=n\sec ]\] \[\therefore \]      \[\frac{{{s}_{n}}}{s}=\frac{\frac{a}{2}(2n-1)}{a{{n}^{2}}/2}=\frac{2}{n}-\frac{1}{{{n}^{2}}}\]


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