Question

a body starts from rest with an acceleration a1. After 2s another body starts from rest with an acceleration a2.If they travel equal distances in the 5th sec.after the start of body A .Find a1÷a2. Full explanation

Answer 1

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Answer 2

Answer:

The ratio of a₁ and a₂ is 5:9

Explanation:

For body A:

Acceleration of body a = a₁

           Initial Velocity, u = 0

                    Time taken = t

Using second equation of motion:

$s(t)=ut+\dfrac{1}{2}at^2$

$s(t)=\dfrac{1}{2}a_1t^2$

Distance travel in 5th second:

$d=s(5)-s(4)$

$d=\dfrac{1}{2}a_1\cdot 5^2-\dfrac{1}{2}a_1\cdot 4^2$

$d=4.5a_1$[/tex]

For body B:

Acceleration of body a = a₂

           Initial Velocity, u = 0

                    Time taken = t-2

Using second equation of motion:

$s(t)=ut+\dfrac{1}{2}at^2$

$s(t)=\dfrac{1}{2}a_2(t-2)^2$

Distance travel in 5th second:

$d=s(5)-s(4)$

$d=\dfrac{1}{2}a_2\cdot 3^2-\dfrac{1}{2}a_2\cdot 2^2$

$d=2.5a_2$[/tex]

We are given both body traveled same distance in 5th seconds.

$4.5a_1=2.5a_2$[/tex]

$\dfrac{a_1}{a_2}=\dfrac{2.5}{4.5}$

$\dfrac{a_1}{a_2}=\dfrac{5}{9}$

Hence, The ratio of a₁ and a₂ is 5:9