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9th Class Science Time and Motion Question Bank Motion IIT JEE Objective Problems

  • question_answer
    A starts from rest and moves with acceleration\[{{a}_{1}}\]. Two seconds later, B starts from rest and moves with an acceleration\[{{a}_{2}}\]. If the displacement of A in the\[{{5}^{\text{th}}}\]second is the same as that of B in the same interval, the ratio of\[{{a}_{1}}\]to\[{{a}_{2}}\]is

    A)  9 : 5                                      

    B)  5 : 9

    C)  1 : 1                                      

    D)  1 : 3

    Correct Answer: B

    Solution :

    Distance travelled in nth second. \[{{S}_{n}}=u+\frac{1}{2}a(2n-1)\] For first body distance covered in\[=50m+50m=100m.\]second. \[{{S}_{1}}=0+\frac{1}{2}{{a}_{1}}(2\times 5-1)=\frac{9}{2}{{a}_{1}}\] Body B stars after 2 sec Distance covered by second body in 5th second of motion of A = Distance covered by second body B in 3rd second \[{{S}_{2}}=0+\frac{1}{2}{{a}_{2}}(2\times 3-1)=\frac{5}{2}{{a}_{2}}\] given\[{{S}_{1}}={{S}_{2}}\Rightarrow \frac{9}{a}{{a}_{1}}=\frac{5}{2}{{a}_{1}}\Rightarrow \frac{{{a}_{1}}}{{{a}_{2}}}=\frac{5}{9}\]


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