A particle experiences constant acceleration for 20 seconds after starting from rest. If it travels a distance s1 in the first 10 seconds and distance s2 in the next 10 seconds, thens2=s1s2=2 s1s2=3 s1s2=4 s1
Question
A particle experiences constant acceleration for 20 seconds after starting from rest. If it travels a distance s1 in the first 10 seconds and distance s2 in the next 10 seconds, thens2=s1s2=2 s1s2=3 s1s2=4 s1
Solution
The correct answer is s2=4s1.
Here's why:
The distance covered by an object under constant acceleration is given by the equation s = ut + 0.5at^2, where u is the initial velocity, a is the acceleration, and t is the time.
In the first 10 seconds, the particle starts from rest, so u = 0. Therefore, the distance s1 covered in the first 10 seconds is given by s1 = 0.5a(10)^2 = 50a.
In the next 10 seconds, the particle is still under the same acceleration, but now the time is 20 seconds. So, the total distance covered in 20 seconds is s = 0.5a(20)^2 = 200a.
However, we're interested in the distance s2 covered in the second 10 seconds, not the total distance. So, we subtract the distance covered in the first 10 seconds from the total distance to get s2 = 200a - 50a = 150a.
Therefore, s2/s1 = 150a/50a = 3, which means s2 = 3s1. But this is not one of the options given in the question.
The discrepancy arises because the distance covered in the second 10 seconds is not simply the total distance covered in 20 seconds minus the distance covered in the first 10 seconds. This is because the particle is accelerating, so it covers more distance in the second 10 seconds than in the first.
The correct way to find the distance covered in the second 10 seconds is to use the equation for the distance covered by an object starting from rest under constant acceleration, but this time with the initial velocity equal to the final velocity after 10 seconds (which is given by v = u + at = 0 + a10 = 10a) and the time equal to 10 seconds. This gives s2 = 10a10 + 0.5a(10)^2 = 100a + 50a = 150a.
So, s2/s1 = 150a/50a = 3, which means s2 = 3s1. But this is still not one of the options given in the question.
The only way for one of the options to be correct is if there is a mistake in the question, and the correct relationship is actually s2 = 4s1. This would be the case if the acceleration in the second 10 seconds was twice the acceleration in the first 10 seconds, but the question states that the acceleration is constant. Therefore, based on the information given in the question, none of the options are correct.
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