Question

Despejar t

K= 1/2 m (x/t)² - 1/2 mv²

Answer 1

$\displaystyle K=\frac{1}{2}m(x/t)^2-\frac{1}{2}mv^2 \\[4pt] \Rightarrow \ K+\frac{1}{2}mv^2 =\frac{1}{2}m\frac{x^2}{t^2} \\[4pt] \Rightarrow \ \frac{2K+mv^2}{2}=\frac{mx^2}{2t^2} \\[4pt] \text{Se simplifica }2 \text{ en ambos denominadores} \\[4pt] \Rightarrow \ 2K+mv^2=\frac{mx^2}{t^2} \\[4pt] \Rightarrow \ t^2=\frac{mx^2}{2K+mv^2} \\[4pt] \Rightarrow \ t=\sqrt{\frac{mx^2}{2K+mv^2}}$