A) (velocity)\[^{3/2}\]
B) (distance)2
C) (distance)\[^{-2}\]
D) (velocity)\[^{\text{2/3}}\]
Correct Answer: A
Solution :
Given, distance \[x={{(t+5)}^{-1}}\] ...(i) Differentiating Eq. (i) w.r.t. t, we get \[\frac{dx}{dt}=(v)=\frac{-1}{{{(t+5)}^{2}}}\] ...(ii) Again, differentiating Eq. (i) w.r.t. t, we get \[\frac{{{d}^{2}}x}{d{{t}^{2}}}=(a)=\frac{2}{{{(t+5)}^{3}}}\] ...(iii) Comparing Eqs. (ii) and (iii), we get \[(a)\propto {{(v)}^{3/2}}\]
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