Motion In A Straight Line Ques 10
10. A particle moves a distance $x$ in time t according to equation $x=(t+5)^{-1}$. The acceleration of particle is proportional to:
[2010]
(a) (velocity) $3 / 2$
(b) (distance)$^{2}$
(c) $(\text{ distance })^{-2}$
(d) $(\text{velocity})^{2 / 3}$
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Answer:
Correct Answer: 10.(a)
Solution:
- (a) distance $x=\frac{1}{t+5}$
$\therefore \quad$ velocity $v=\frac{d x}{d t}=\frac{-1}{(t+5)^{2}}$
$\therefore \quad$ acceleration $a=\frac{d^{2} x}{d t^{2}}=\frac{2}{(t+5)^{3}}=2 x^{3}$
Therefore, $v^{3 / 2}=-(t+5)^{-3}$
So, $a \propto v^{3 / 2}$