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

Thanks, in advance.

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- Dec 19th 2009, 07:47 AMDJSmith3000Help 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

Thanks, in advance. - Dec 19th 2009, 07:52 AMPlato
- Dec 19th 2009, 08:01 AMGrandad
Hello DJSmith3000

Welcome to Math Help Forum!I'm not sure that this really is a question. The equation

$\displaystyle v^2=u^2+2as$gives the relationship between the initial ($\displaystyle u$) and final ($\displaystyle v$) velocities, when a body moving with a constant acceleration ($\displaystyle a$) moves through a certain distance ($\displaystyle s$).

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 $\displaystyle F$ acts on a body of mass $\displaystyle m$, giving it a (constant) acceleration $\displaystyle a$, we have:

$\displaystyle F = ma$and so if the body now moves through a distance $\displaystyle s$ in the direction of the force, the work done on the body is:

$\displaystyle Fs = mas$This increases the body's KE from $\displaystyle \tfrac12mu^2$ to $\displaystyle \tfrac12mv^2$, where $\displaystyle u$ and $\displaystyle v$ are the initial and final velocities. So, using the Work-Energy Principle, we have:

$\displaystyle mas = \tfrac12mv^2 - \tfrac12mu^2$Grandad

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

- Dec 19th 2009, 08:18 AMDJSmith3000
im sorry, i forgot to put that part...

i have to make U then S the subject

thanks for replying :) - Dec 19th 2009, 01:31 PMGrandad
Hello DJSmith3000$\displaystyle v^2=u^2+2as$

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

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

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

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

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

Grandad - Dec 19th 2009, 01:53 PMDJSmith3000
Thank you so much =]