Question

A body of mass $m$ starting from rest from origin moves along $x$-axis with constant power (P). Calculate relation between velocity and distance:-

• A. $x \propto v ^{1 / 2}$
• B. $x \propto v^{2}$
• C. $x \propto v$
• D. $x \propto v^{3}$

Answer 1

Answer: (D)

$P=$ mav
$\Rightarrow P=m\left(v \frac{d v}{d x}\right) \cdot v$
$\Rightarrow m v^{2} d v=P d x $
$\Rightarrow \frac{m v^{3}}{3}=p x $
$\Rightarrow v \propto x^{1 / 3}$