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SOLUTION
We want to solve for v in
[tex]F=\frac{mv^2}{R}[/tex]This means we should make v the subject, that is make it stand alone. This becomes
[tex]\begin{gathered} F=\frac{mv^2}{R} \\ m\text{ultiply both sides by }R,\text{ we have } \\ F\times R=\frac{mv^2}{R}\times R \\ R\text{ cancels R in the right hand side of the equation we have } \\ FR=mv^2 \end{gathered}[/tex]Next, we divide both sides by m, we have
[tex]\begin{gathered} FR=mv^2 \\ \frac{FR}{m}=\frac{mv^2}{m} \\ m\text{ cancels m, we have } \\ \frac{FR}{m}=v^2 \\ v^2=\frac{FR}{m} \end{gathered}[/tex]Lastly, we square root both sides we have
[tex]\begin{gathered} v^2=\frac{FR}{m} \\ \sqrt[]{v^2}=\sqrt[]{\frac{FR}{m}} \\ \text{square cancels square root, we have } \\ v=\sqrt[]{\frac{FR}{m}} \end{gathered}[/tex]Hence the answer is
[tex]v=\sqrt[]{\frac{FR}{m}}[/tex]
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