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 distance in the 5th second after the start of A, then find the ratio a1:a2.?

Question

Answer

Answer

Answer

5/9

Answer

5/9 ans

Answer

Problem Statement: 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 distance in the 5th second after the start of A, then find the ratio a1:a2?

Solution:

Let the distance travelled by both A and B in the first 5 seconds be S.

Calculating Distance Traveled by A in 5 seconds:

In 5 seconds, the distance travelled by A can be calculated using the following formula:

S = ut + 1/2 at^2

Where, u = initial velocity = 0
t = time = 5 seconds
a = acceleration = a1

Therefore, S = 0 + 1/2 a1 (5)^2 = 12.5 a1

Calculating Distance Traveled by B in 5 seconds:

In 5 seconds, the distance travelled by B can be calculated using the following formula:

S = ut + 1/2 at^2

Where, u = initial velocity = 0
t = time = 3 seconds (since B starts after 2 seconds)
a = acceleration = a2

Therefore, S = 0 + 1/2 a2 (3)^2 = 4.5 a2

Since both A and B travel the same distance in the 5th second, we can say that their velocities are equal at the end of the 5th second.

Calculating Velocity of A at the end of 5 seconds:

The velocity of A at the end of 5 seconds can be calculated using the following formula:

v = u + at

Where, u = initial velocity = 0
t = time = 5 seconds
a = acceleration = a1

Therefore, v = 0 + a1 (5) = 5 a1

Calculating Velocity of B at the end of 5 seconds:

The velocity of B at the end of 5 seconds can be calculated using the following formula:

v = u + at

Where, u = initial velocity = 0
t = time = 3 seconds (since B starts after 2 seconds)
a = acceleration = a2

Therefore, v = 0 + a2 (3) = 3 a2

Since the velocities of A and B are equal at the end of the 5th second, we can say that:

5 a1 = 3 a2

Therefore, the ratio of a1 to a2 is:

a1/a2 = 3/5

Hence, the ratio of a1 to a2 is 3:5.

Answer

Answer is 5/9.

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