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A particle starts from rest and moves with uniform acceleration. If it covers a distance S1 in the first t1 seconds and a distance S2 in the next t2 seconds, find the ratio S1/S2.

1. S1/S2 = (t1/t2)^2
2. S1/S2 = 1/4
3. S2 = 4S1
4. None of these

Correct answer: S1/S2 = (t1/t2)^2

Solution

For a particle starting from rest and moving with uniform acceleration, the distance covered in time t is given by S = (1/2)at^2. In the first t1 seconds, S1 = (1/2)a(t1)^2. In the next t2 seconds, the total distance covered is S_total = (1/2)a(t1 + t2)^2, so S2 = S_total - S1 = (1/2)a(t1 + t2)^2 - (1/2)a(t1)^2. Simplifying, S2 = (1/2)a[(t1 + t2)^2 - (t1)^2] = (1/2)a[2t1t2 + (t2)^2]. The ratio S1/S2 = (t1^2) / [2t1t2 + t2^2] = (t1/t2)^2.

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