Rearranging an Equation

Date: 3/25/96 at 4:13:4
From: michael laird
Subject: rearrange the formula

                             2
rearrange the formula E=1/2mv      to make v the subject

Michael

Date: 3/25/96 at 11:4:29
From: Doctor Ethan
Subject: Re: rearrange the formula

Hey Michael,

Well, your question got a little mixed up in transit but I am assuming 
that 2 out there by itself should be the power of the v

so it reads  E = 1/2 m v^2  right?

If so, then here is what we are going to do.

First we are going to isolate the v^2, then get rid of the ^2.

When you work with equations like this you can pretty much do 
whatever you want as long as you do it the same way to both 
sides. For instance, I can multiply both sides by 2 to get

2E = 2 (1/2 m v^2)

And that will cancel with the 1/2 on the right side, so we have

2E =  m v^2    

And now, in a similar move, we can divide both sides by m, and we 
have

2E/m  = (m v^2)/m

Again the m's will cancel on the left and we have

2E/m = v^2

So now we are pretty close. All we have to do is get rid of the ^2.
To do that we need to take the square root of both sides.  However, 
here we have to be careful.  The square root of a number can be 
positive or negative.

So we cannot simply assume that things are positive.  Usually in an 
applied problem, there will be limitations on your answer so that 
you will know, but that is not the case here.

So we have that (pos or neg) Sqrt[ 2E/m] = v

Where Sqrt[  ]  means square root.

Hope that this helps.

-Doctor Ethan,  The Math Forum