A) \[{{s}_{2}}=\text{ }{{s}_{1}}\]
B) \[{{s}_{2}}=\text{ }2{{s}_{1}}\]
C) \[{{s}_{2}}=\text{ }3{{s}_{1}}\]
D) \[{{s}_{2}}=\text{ }4{{s}_{1}}\]
Correct Answer: C
Solution :
From equation of motion, we get \[s=ut+\frac{1}{2}a{{t}^{2}}\] where u is initial velocity, a the acceleration and t the time. Given, u = 0 (from rest), t = 10 s, \[s={{s}_{1}}\] \[\therefore \] \[{{s}_{1}}=0+\frac{1}{2}\,a\,{{(10)}^{2}}=50a\] ... (i) Velocity after 10 s v = u + ac \[v=0+a\times 10=10a\] Distance covered in next 10 s is \[{{s}_{2}}=vt+\frac{1}{2}a{{t}^{2}}\] \[{{s}_{2}}=10a\times 10+\frac{1}{2}\times a\times {{(10)}^{2}}\] \[\Rightarrow \] \[{{s}_{2}}=3{{s}_{1}}\] ... (ii) From Eqs. (i) and (ii), we get \[\frac{{{s}_{2}}}{{{s}_{1}}}=\frac{150\,a}{50\,a}=\frac{3}{1}\] \[\Rightarrow \] \[{{s}_{2}}=3{{s}_{1}}\]
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