Kinematics Question 365

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

Options:

A) $ {{( velocity )}^{3/2}} $

B) $ {{( distance )}^{2}} $

C) $ {{( distance )}^{-2}} $

D) $ {{( velocity )}^{2/3}} $

Show Answer

Answer:

Correct Answer: A

Solution:

$ \text{x=}\frac{1}{\text{t+5}}\text{ }\therefore v=\frac{dx}{dt}=\frac{-1}{{{( t+5 )}^{2}}} $
$ \therefore a=\frac{d^{2}x}{dt^{2}}=\frac{2}{{{( t+5 )}^{3}}}=2x^{3} $

$ \text{Now }\frac{1}{( t+5 )}\propto {{v}^{\frac{1}{2}}} $
$ \therefore \frac{1}{{{( t+5 )}^{3}}}\propto {{v}^{\frac{3}{2}}}\propto a $



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