Question

Rewrite the equation to easily determine the velocity of an object. solve the Equation for v

Answer 1

In order to solve for v in the given equation, follow these steps:

1. Divide both sides of the equation by "m"

`\begin{gathered} E=(1)/(2)mv^2 \\ (E)/(m)=(1)/(2)(mv^2)/(m) \\ (E)/(m)=(1)/(2)(m)/(m)v^2 \\ (E)/(m)=(1)/(2)v^2 \end{gathered}`

2. Multiply both sides by 2

`\begin{gathered} (E)/(m)*2=(1)/(2)v^2*2 \\ 2(E)/(m)=(2)/(2)v^2 \\ 2(E)/(m)=v^2 \end{gathered}`

3. in order to get rid of the exponent of v, take the square root on both sides

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

Then, v = √(2E/m)