# Math Help - Help with Transposition

1. ## 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

2. 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.

3. Hello DJSmith3000

Welcome to Math Help Forum!
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:
$mas = \tfrac12mv^2 - \tfrac12mu^2$

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

4. im sorry, i forgot to put that part...
i have to make U then S the subject

5. Hello DJSmith3000
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 $v^2=u^2+2as$

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

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