First slide

Rectilinear Motion

Question

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

Moderate

A

5:9
B

5:7
C

9:5
D

9:7

Solution

$g i v e n i n i t i a l v e l o c i t y u = 0; a c c e l e r a t i o n = a_{1}; t i m e n = 5 s e c; s u b s t i t u t e i n, S_{n} = u + \frac{a}{2} (2 n - 1) - - - (1) x b o d y A : S = 0 + \frac{1}{2} a_{1} (2 \times 5 - 1) = \frac{9 a_{1}}{2} ---(3) body B:→ g i v e n i n i t i a l v e l o c i t y u = 0; a c c e l e r a t i o n = a_{2}; t i m e n = 3 s e c; s u b s t i t u t e i n e q u a t i o n (1) S = 0 + \frac{1}{2} a_{2} (2 \times 3 - 1) = \frac{5 a_{2}}{2} ---(4) e q u a t e e q u a t i o n s (3) a n d (4) \frac{9 a_{1}}{2} = \frac{5 a_{2}}{2} ⇒ \frac{a_{1}}{a_{2}} = \frac{5}{9}$

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