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. ${\left(velocity\right)}^{3/2}$
• B. ${\left(Distance\right)}^2$
• C. ${\left(Distance\right)}^{-2}$
• D. ${\left(velocity\right)}^{2/3}$

Answer 1

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

The distance traveled by the particle is given by the relation $x=(t+5{)}^{-1}$

As we know that Velocity $v=\frac{dx}{dt}$

$\Rightarrow v=-1(t+5{)}^{-2}$

$\Rightarrow v\propto (t+5{)}^{-2}$ ....$\left(1\right)$

Also Acceleration $a=\frac{dv}{dt}$

$\Rightarrow a=(-1)(-2)(t+5{)}^{-3}=2(t+5{)}^{-3}$

$\Rightarrow a\propto (t+5{)}^{-3}$ ...$\left(2\right)$

Using equation $\left(1\right)$ and $\left(2\right)$ we can write that $a=\left(\right(t+5{)}^{-2}{)}^{3/2}$

$\Rightarrow$ $a=(v{)}^{3/2}$

Hence Correct option is $A$