A) \[{{x}_{2}}=3{{x}_{1}}\]
B) \[{{x}_{2}}={{x}_{1}}\]
C) \[{{x}_{2}}=4{{x}_{1}}\]
D) \[{{x}_{2}}=2{{x}_{1}}\]
Correct Answer: A
Solution :
: As the body starts from rest, \[\therefore \] \[u=0\] Let a be constant acceleration of the body. Distance travelled by the body in (t/2) s is \[{{v}^{2}}\] \[{{x}_{1}}=\frac{1}{2}a{{\left( \frac{t}{2} \right)}^{2}}=\frac{1}{8}a{{t}^{2}}\] ??(i) Distance travelled by the body in t s is \[{{x}_{1}}+{{x}_{2}}=\frac{1}{2}a{{t}^{2}}=4{{x}_{1}}\] (Using (i)) \[\therefore \] \[{{x}_{2}}=4{{x}_{1}}-{{x}_{1}}=3{{x}_{1}}\]
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