A body A starts from rest with an acceleration a1. After 2 s another body B starts from rest with an acceleration a2. If they travel equal distances in 5 s, after the starts of A, the ratio a1: a2 will be equal to:

Question

A body A starts from rest with an acceleration a1. After 2 s another body B starts from rest with an acceleration a2. If they travel equal distances in 5 s, after the starts of A, the ratio a1: a2 will be equal to: (A) 9: 5 (B) 5: 7 (C) 5: 9 (D) 7: 9

Tardigrade Admin · Accepted Answer

The distance covered by the body in the

n

th second of motion is

S_{n} = u + \frac{a}{2} (2 n - 1)

where

u

is initial velocity and

a

is acceleration. Distance covered by the body

A

in 5 th second after its start, with acceleration

a_{1}

, is

(S_{5})_{A} = 0 + \frac{a _{1}}{2} (2 \times 5 - 1) = \frac{9 a _{1}}{2}

Time taken by second body

= 5 - 2 = 3 s

(S_{3})_{B} = 0 + \frac{a _{2}}{2} (2 \times 3 - 1) = \frac{5 a _{2}}{2}

Given,

(S_{5}) A = (S_{3})_{B}

∴ \frac{a _{1}}{a _{2}} = \frac{5}{9}

Q. A body $A$ starts from rest with an acceleration $a_{1}$ . After $2 s$ another body $B$ starts from rest with an acceleration $a_{2}$ . If they travel equal distances in $5 s$ , after the starts of $A$ , the ratio $a_{1} : a_{2}$ will be equal to:

$9 : 5$

$5 : 7$

$5 : 9$

$7 : 9$

Q. A body A starts from rest with an acceleration a1​. After 2s another body B starts from rest with an acceleration a2​. If they travel equal distances in 5s, after the starts of A, the ratio a1​:a2​ will be equal to:

9:5

5:7

5:9

7:9

Q. A body $A$ starts from rest with an acceleration $a_{1}$ . After $2 s$ another body $B$ starts from rest with an acceleration $a_{2}$ . If they travel equal distances in $5 s$ , after the starts of $A$ , the ratio $a_{1} : a_{2}$ will be equal to:

$9 : 5$

$5 : 7$

$5 : 9$

$7 : 9$