Question

K=1/2mv^2 -1/2 mx^2. solve for x

Answer 1

Answer:

$x=\sqrt{v^2 -\frac{2k}{m}}$

Explanation:

Equation Solving

The procedure to solve an equation consists in trying to isolate the required variable by applying algebra and / or elemental properties of some functions. If not possible, then we could use formulas or iterative approaches.

The equation to solve is

$\displaystyle k=\frac{1}{2}mv^2 -\frac{1}{2} mx^2$

Rearranging

$\displaystyle \frac{1}{2} mx^2=\frac{1}{2}mv^2 -k$

Multiplying by 2/m

$\displaystyle x^2=v^2 -\frac{2k}{m}$

Solving for x

$\displaystyle \boxed{x=\sqrt{v^2 -\frac{2k}{m}}}$