A particle is projected with velocity r^o along x - axis . The deceleration on the particle is proportional to the square of the distance from the origin i.e., a \propto x^{2} . The distance at which the particle stops is
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\(a \frac{dv}{dt} - \frac{dv}{dx} \frac{dx}{dt}\) \(-\nu \frac{\partial v}{\partial x} = - \alpha x^{2}\) (given)
⇒ ⇒ \(\int_c^v \mu \alpha v \quad - \quad x \int_c^v x = \alpha x\) ⇒ ⇒ \(\nu = 10^{12} = -c \left| \begin{matrix} x^2 \\ 3 \end{matrix} \right|\)
⇒ ⇒ \(\frac{v_x^2}{2} - \frac{r^5}{3}\) ⇒ ⇒ \(s \left| \frac{3v^{2}}{2x} \right|^{\frac{1}{3}}\)
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