The rate of doing work by force acting on a particle moving along x-axis depends on position x of particle and is equal to 2 x. The velocity of particle is given by expression

Question

The rate of doing work by force acting on a particle moving along x-axis depends on position x of particle and is equal to 2 x. The velocity of particle is given by expression (A) [(3 x2/m)]1 / 3 (B) [(3 x2/2 m)]1 / 3 (C) ((2 m x/9))1 / 2 (D) [(m x2/3)]1 / 2

Tardigrade Admin · Accepted Answer

P=(F ⋅ d x/d t) =m((v d v/d x)) v=2 x m ∫ v2 d v=∫ 2 x d x (m v3/3)=x2 v=((3 x2/m))(1/3)

Q. The rate of doing work by force acting on a particle moving along $x$ -axis depends on position $x$ of particle and is equal to $2 x$ . The velocity of particle is given by expression

$[\frac{3 x ^{2}}{m}]^{1/3}$

$[\frac{3 x ^{2}}{2 m}]^{1/3}$

$(\frac{2 m x}{9})^{1/2}$

$[\frac{m x ^{2}}{3}]^{1/2}$

$P = \frac{F \cdot d x}{d t}$
$= m (\frac{v d v}{d x}) v = 2 x$
$m \int v^{2} d v = \int 2 x d x$
$\frac{m v ^{3}}{3} = x^{2}$
$v = (\frac{3 x ^{2}}{m})^{\frac{1}{3}}$

Q. The rate of doing work by force acting on a particle moving along x-axis depends on position x of particle and is equal to 2x. The velocity of particle is given by expression

[m3x2​]1/3

[2m3x2​]1/3

(92mx​)1/2

[3mx2​]1/2