A body starts from rest with an acceleration . After 2 seconds, another body starts from rest with an acceleration . If they travel equal distances in the 5th second, after the start of A, then the ratio is equal to

Question

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

Smart Achievers · Accepted Answer

(1)

$Time taken by body A, t_{1} = 5 s$

$Acceleration of body A = a_{1}$

$Time taken by body B, t_{2} = 5 - 2 = 3 s$

$Acceleration of body B = a_{2}$

Distance covered by first body in $5^{th}$ second after its start,

$S_{5} = u + \frac{a_{1}}{2} (2 t_{1} - 1) = 0 + \frac{a_{1}}{2} (2 \times 5 - 1) = \frac{9}{2} a_{1}$

Distance covered by the second body in the $3^{rd}$ second after its start,

$S_{3} = u + \frac{a_{2}}{2} (2 t_{2} - 1) = 0 + \frac{a_{2}}{2} (2 \times 3 - 1) = \frac{5}{2} a_{2}$

Since $S_{5} = S_{3}$ $∴$ $\frac{9}{2} a_{1} = \frac{5}{2} a_{2}$ or $a_{1} : a_{2} = 5 : 9$

Solution

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

1 5 : 9

2 5 : 7

3 9 : 5

4 9 : 7

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