Answer:
[tex]\large\boxed{v=\pm\sqrt{\dfrac{LT}{m}}}[/tex]
Step-by-step explanation:
[tex]\dfrac{mv^2}{L}=T\qquad\text{multiply both sides by}\ L\\\\L\!\!\!\!\diagup^1\cdot\dfrac{mv^2}{L\!\!\!\!\diagup_1}=LT\\\\mv^2=LT\qquad\text{divide both sides by}\ m\\\\\dfrac{m\!\!\!\!\diagup^1v^2}{m\!\!\!\!\diagup_1}=\dfrac{LT}{m}\\\\v^2=\dfrac{LT}{m}\qquad\text{square root of both sides}\\\\\sqrt{v^2}=\sqrt{\dfrac{LT}{m}}\qquad\text{use}\ \sqrt{a^2}=|a|\\\\|v|=\sqrt{\dfrac{LT}{m}}\Rightarrow v=\pm\sqrt{\dfrac{LT}{m}}[/tex]
