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  4. A particle moves a distance x in time t according to equation x=(t+5)-1. The acceleration of particle is proportional to

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Q. A particle moves a distance $ x $ in time t according to equation $ x={{(t+5)}^{-1}}. $ The acceleration of particle is proportional to

VMMC MedicalVMMC Medical 2012

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}} $