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Q.

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

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a

9:1

b

1:3

c

5:9

d

3:1

answer is A.

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Detailed Solution

Distance travelled by A in 5^th second,

$s_{A} = 0 + \frac{a_{1}}{2} (2 \times 5 - 1) = \frac{9}{2} a_{1}$

Distance travelled by B in 3^rd second,

$s_{B} = 0 + \frac{a_{2}}{2} (2 \times 3 - 1) = \frac{5}{2} a_{2}$

As per question, $s_{A} = s_{B}$

So $\frac{9}{2} a_{1} = \frac{5}{2} a_{2}$

Or $\frac{a_{1}}{a_{2}} = \frac{5}{9}$

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A body A starts from rest with an acceleration a1. After two seconds, another body B starts from rest with an acceleration a2. If they travel equal distances in the 5th second after the start of A, then the ratio of a1:a2 is equal to