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 $
