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
Thanks, in advance.
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:
$\displaystyle mas = \tfrac12mv^2 - \tfrac12mu^2$
$\displaystyle \Rightarrow v^2=u^2+2as$
Grandad