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Differential Equations

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An Object in a Conservative Field

DIFFEQ-4WQYD1

An object with initial velocity $v_0$ slows down in an external conservative field. Under this external field, the acceleration of the object is $a(x)=-\mu x^2$ where $x$ is the distance from​ the initial position of the object. Find the expression of the velocity of the object in terms of $x$.

A

$v_0-\mu x^2 t$

B

$v_0-\cfrac{1}{3}\mu x^3$

C

$\sqrt{v_0^2-\cfrac{1}{3}\mu x^3}$

D

$\sqrt{v_0^2-\cfrac{2}{3}\mu x^3}$