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Question: A body A starts from rest with an acceleration \(a_{1}\). After 2 seconds, another body B starts fro...

A body A starts from rest with an acceleration a1a_{1}. After 2 seconds, another body B starts from rest with an acceleration a2a_{2}. If they travel equal distances in the 5th second, after the start of A, then the ratio a1:a2a_{1}:a_{2} is equal to

A

5 : 9

B

5 : 7

C

9 : 5

D

9 : 7

Answer

5 : 9

Explanation

Solution

By using Sn=u+a2(2n−1)S_{n} = u + \frac{a}{2}(2n - 1), Distance travelled by body A in 5th second = 0+a12(2×5−1)0 + \frac{a_{1}}{2}(2 \times 5 - 1)

Distance travelled by body B in 3rd second is

=0+a22(2×3−1)0 + \frac{a_{2}}{2}(2 \times 3 - 1)

According to problem :0+a12(2×5−1)0 + \frac{a_{1}}{2}(2 \times 5 - 1) = 0+a22(2×3−1)0 + \frac{a_{2}}{2}(2 \times 3 - 1) ⇒ 9a1=5a2⇒a1a2=599a_{1} = 5a_{2} \Rightarrow \frac{a_{1}}{a_{2}} = \frac{5}{9}