Deriving the Equation v^2=U^2+2as using Physics Principles

[stuwalshe]

Hi, I need help with the following, I don't think it is too hard but I don't know how to approach it.

given that v=u+at and s=ut+1/2at^2

show that v^2=U^2+2as

thankyou

 

[cristo]

Have you tried anything yet? Please note that for homework questions you must show your work before we can help you.

Here's a hint: look at the variables in the equation you are trying to show. There is one variable that is present in the first two equations, but not in the final one. Can you write one of the first two in a way such that you can eliminate this variable?

 

[stuwalshe]

cristo
I can see that t is common to both the first equations but not in the 3rd, I guess they cancel out some how, I have made t the subject of the first equation. i.e

v=u+at == t=(v-u)/a.

I think I then have to substitute this into the second equation, this is where I come unstuck, I am unsure of how to substitute the 2 equations together.
t=(v-u)/a
s=ut+1/2at^2

do I then multiply both sides of each equation? i.e

st=ut+1/2at^2(v-u)/a ?

if so then I am unsure how to eliminate the t's and how to get the u^2
thankyou

 

[cristo]

cristo
I can see that t is common to both the first equations but not in the 3rd, I guess they cancel out some how, I have made t the subject of the first equation. i.e

v=u+at == t=(v-u)/a.

Good.

I think I then have to substitute this into the second equation, this is where I come unstuck

Good idea. The easiest way to proceed is to take t=(v-u)/a and substitute it directly into the equation s=ut+1/2at^2. So, you would obtain $$s=u\cdot\left(\frac{(v-u)}{a}\right)+\frac{1}{2}a\left(\frac{(v-u)}{a}\right)^2$$

Can you continue from here by simplifying?

 

[stuwalshe]

thanks for your help, could you please take me back a step and explain how you got rid of the t's,

For some reason I am really struggling with this one, when I look to simplify the expression you came up with, I can't seam to think of how to get to where I want to be.
do you think you could start me off.

stu

 

[stuwalshe]

sorry mate, I was being silly, I understand how the t's cancel, like you said you just substituted them, I think I have done too much today, I still can't see how to simplify the equation though, if you could start me off that would be great.

stu

 

[cristo]

Well, I presume you can multiply out the first term. For the second term take out a^2 from the denominator, and then expand (v-u)^2 using whichever technique you have learnt.

 

[stuwalshe]

i expanded to

2as=(uv-u^2)/au + (v^2-2uv+v^2)/a^2

I do not think this is correct though because nothing seams to cancel
sorry about this
stu