# Help with Transposition

• Dec 19th 2009, 07:47 AM
DJSmith3000
Help with Transposition
Hello, I have joined this forum in hopes of finding the answers to my question, is their anybody who can spare the time to give me a quick run through this question?

V^2 = U^2 + 2as

• Dec 19th 2009, 07:52 AM
Plato
Quote:

Originally Posted by DJSmith3000
Hello, I have joined this forum in hopes of finding the answers to my question, is their anybody who can spare the time to give me a quick run through this question?
V^2 = U^2 + 2as

What is the question?
I see an equation. But no question..
Tell what you have been asked to do to or with that equation.
• Dec 19th 2009, 08:01 AM
Hello DJSmith3000

Welcome to Math Help Forum!
Quote:

Originally Posted by DJSmith3000
Hello, I have joined this forum in hopes of finding the answers to my question, is their anybody who can spare the time to give me a quick run through this question?

V^2 = U^2 + 2as

I'm not sure that this really is a question. The equation
$v^2=u^2+2as$
gives the relationship between the initial ( $u$) and final ( $v$) velocities, when a body moving with a constant acceleration ( $a$) moves through a certain distance ( $s$).

The easiest way to derive it is to use the Work-Energy Principle, which states that the work done on a body is equal to the increase in its Kinetic Energy. Thus, if a constant force $F$ acts on a body of mass $m$, giving it a (constant) acceleration $a$, we have:
$F = ma$
and so if the body now moves through a distance $s$ in the direction of the force, the work done on the body is:
$Fs = mas$
This increases the body's KE from $\tfrac12mu^2$ to $\tfrac12mv^2$, where $u$ and $v$ are the initial and final velocities. So, using the Work-Energy Principle, we have:
$mas = \tfrac12mv^2 - \tfrac12mu^2$

$\Rightarrow v^2=u^2+2as$
• Dec 19th 2009, 08:18 AM
DJSmith3000
im sorry, i forgot to put that part...
i have to make U then S the subject
• Dec 19th 2009, 01:31 PM
Hello DJSmith3000
Quote:

Originally Posted by DJSmith3000
im sorry, i forgot to put that part...
i have to make U then S the subject

$v^2=u^2+2as$

$\Rightarrow v^2-2as=u^2$

$\Rightarrow u = \sqrt{v^2-2as}$

And $v^2=u^2+2as$

$\Rightarrow v^2-u^2=2as$

$\Rightarrow s = \frac{v^2-u^2}{2a}$