Question

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

Answer 1

`x=\sqrt{v^2 -(2k)/(m)}`

Step-by-step 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=(1)/(2)mv^2 -(1)/(2) mx^2`

Rearranging

`\displaystyle (1)/(2) mx^2=(1)/(2)mv^2 -k`

Multiplying by 2/m

`\displaystyle x^2=v^2 -(2k)/(m)`

Solving for x

`\displaystyle \boxed{x=\sqrt{v^2 -(2k)/(m)}}`