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

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 v2 (C) x propto v (D) x propto v3

Tardigrade Admin · Accepted Answer

P= mav ⇒ P=m(v (d v/d x)) ⋅ v ⇒ m v2 d v=P d x ⇒ (m v3/3)=p x ⇒ v propto x1 / 3

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

$x \propto v^{1/2}$

$x \propto v^{2}$

$x \propto v$

$x \propto v^{3}$

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

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

x∝v1/2

x∝v2

x∝v

x∝v3