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(B) According to the Work-Energy Theorem,the total work done by all forces is equal to the change in kinetic energy: $W = \Delta KE = \frac{1}{2} m v_

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$\frac{1}{2} m a^2 d$

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(B) According to the Work-Energy Theorem,the total work done by all forces is equal to the change in kinetic energy: $W = \Delta KE = \frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2$.Given the velocity function $v = a\sqrt{x}$.At $x = 0$,the initial velocity $v_i = a\sqrt{0} = 0$.At $x = d$,the final velocity $v_f = a\sqrt{d}$.Substituting these values into the work-energy equation:$W = \frac{1}{2} m (a\sqrt{d})^2 - \frac{1}{2} m (0)^2$.$W = \frac{1}{2} m a^2 d - 0$.$W = \frac{1}{2} m a^2 d$.

$A$ particle of mass $m$ moves with a velocity $v = a\sqrt{x}$,where $a$ is a constant and $x$ is the displacement. Find the total work done by all forces during the displacement from $x = 0$ to $x = d$.

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