A) \[{{\left( velocity \right)}^{3/2}}\]
B) \[{{\left( distance \right)}^{2}}\]
C) \[{{\left( distance \right)}^{-2}}\]
D) \[{{\left( velocity \right)}^{2/3}}\]
Correct Answer: A
Solution :
\[\text{x=}\frac{\text{1}}{\text{t+5}}\text{ }\therefore v=\frac{dx}{dt}=\frac{-1}{{{\left( t+5 \right)}^{2}}}\] \[\therefore a=\frac{{{d}^{2}}x}{d{{t}^{2}}}=\frac{2}{{{\left( t+5 \right)}^{3}}}=2{{x}^{3}}\] \[\text{Now }\frac{1}{\left( t+5 \right)}\propto {{v}^{\frac{1}{2}}}\] \[\therefore \frac{1}{{{\left( t+5 \right)}^{3}}}\propto {{v}^{\frac{3}{2}}}\propto a\]
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