Solve a=-ksqrt{v}

$$a = - k \sqrt { v }$$

Solve for k

$$\left\{\begin{matrix}k=-\frac{a}{\sqrt{v}}\text{, }&v>0\\k\in \mathrm{R}\text{, }&v=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\left(-k\right)\sqrt{v}=a$$

Reorder the terms.

$$-\sqrt{v}k=a$$

The equation is in standard form.

$$\left(-\sqrt{v}\right)k=a$$

Divide both sides by -\sqrt{v}.

$$\frac{\left(-\sqrt{v}\right)k}{-\sqrt{v}}=\frac{a}{-\sqrt{v}}$$

Dividing by -\sqrt{v} undoes the multiplication by -\sqrt{v}.

$$k=\frac{a}{-\sqrt{v}}$$

Divide a by -\sqrt{v}.

$$k=-\frac{a}{\sqrt{v}}$$

Solve for a

$$a=-\sqrt{v}k$$

$$v\geq 0$$