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. $\left[\frac{3 x^{2}}{m}\right]^{1 / 3}$
• B. $\left[\frac{3 x^{2}}{2 m}\right]^{1 / 3}$
• C. $\left(\frac{2 m x}{9}\right)^{1 / 2}$
• D. $\left[\frac{m x^{2}}{3}\right]^{1 / 2}$

Answer 1

Answer: (A)

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