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55:

55 A body starts from rest with an accelerat ion a , after 2 second , another body B status from rest with an acceleration a_{2}. If they travel equal distance in the 5^{th} second. after the start of A, then the ratio a_{1} : a_{2} is equal to:

(A) 5:9 (B) 5:7

(C) 9:5 (D) 9:7

Dear Student ,

For the body ‘A’, the distance travelled in 5^{th} second is,

S_{5} = 0 + ½ a_{1} (2n - 1)

=> S_{5} = 9/2 a_{1} [n = 5]

For the body ‘B’, the distance travelled in the 5^{th} second after the start of A is actually the distance travelled by the body B in the 3^{rd} second, since, B starts 2 s later.

Therefore,

S_{3} = 0 + ½ a_{2} (2n - 1)

=> S_{3} = 5/2 a_{2} [n = 3]

Since, the distance travelled are same,

9/2 a_{1} = 5/2 a_{2}

=> a_{1} : a_{2} = 5 : 9

Regards

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