Question

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

• A. $(\text{velocity}{)}^{3/2}$
• B. $(\text{distance}{)}^2$
• C. $(\text{velocity}{)}^{2/3}$
• D. $(\text{distance}{)}^{-2}$

Answer 1

The correct option is A $(\text{velocity}{)}^{3/2}$

Given, $x=\frac{1}{t+5}$
$\Rightarrow v=\frac{dx}{dt}=-\frac{1}{(t+5{)}^2}$
Thus, acceleration will be
$a=\frac{dv}{dt}=\frac{2}{(t+5{)}^3}$
$\Rightarrow a\propto (\text{velocity}{)}^{3/2}$.