A body travels for 15 sec starting from rest with constant acceleration. If it travels distances S_1, S_2 and S_3 in the first five seconds, second five seconds and next five seconds respectively the relation between S_1, S_2 and S_3 is
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Let a be uniform acceleration of the body.
As \(S = ut + \frac{1}{2}at^{2} = \frac{1}{2}at^{2} \; (\therefore u = 0)\)
Then, \(S_{1} = \frac{1}{2} a (5)^{2}\) …..(i)
\(S_1 + S_2 = \frac{1}{2} a (10)^2 \quad .... (ii) S_1 + S_2 + S_3 = \frac{1}{2} a (15)^2 \quad .... (iii)\)
Subtract (i) from (ii), we get
\[ (S_1 + S_2) - S_1 = \frac{1}{2} a (10)^2 - \frac{1}{2} a (5)^2 \] \[ S_2 = \frac{75}{2} a = 3 S_1 \quad (\text{Using (i)}) \]
Subtract (ii) from (iii), we get
\((S_1 + S_2 + S_3) - (S_1 + S_2) = \frac{1}{2} a (15)^2 - \frac{1}{2} a (10)^2\)
\(S_3 = \frac{125}{2} a = 5S_1 \quad \text{(Using (i))}\)
Thus, \(S_1 = \frac{1}{3} S_2 = \frac{1}{5} S_3\)
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