Question

8. Use the equation E =1- my for the following questions:2(a) Rearrange the equation so that it's solved for vShow your work here:SolutionV

Answer 1

Starting from the equation:

`E=(1)/(2)mv^2`

Multiply both members by 2 to cancel out the factor of 1/2 on the right member of the equation:

`\begin{gathered} \Rightarrow2E=2((1)/(2)mv^2) \\ \Rightarrow2E=mv^2 \end{gathered}`

Divide both members by m to cancel out the factor of m on the right member of the equation:

`\begin{gathered} \Rightarrow(2E)/(m)=(mv^2)/(m) \\ \Rightarrow(2E)/(m)=v^2 \end{gathered}`

Take the square root of both member of the equation to get rid of the exponent of v:

`\begin{gathered} \Rightarrow\sqrt[]{(2E)/(m)}=\sqrt[]{v^2} \\ \Rightarrow\sqrt[]{(2E)/(m)}=v \end{gathered}`

Therefore, the equation rearranged so that it is solved for v is:

`v=\sqrt[]{(2E)/(m)}`