# Physics help

1. Aug 18, 2007

### stuwalshe

Hi, I need help with the following, I dont think it is too hard but I dont know how to approach it.

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

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

thankyou

2. Aug 18, 2007

### cristo

Staff Emeritus

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?

3. Aug 18, 2007

### 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

Last edited by a moderator: Aug 18, 2007
4. Aug 18, 2007

### cristo

Staff Emeritus
Good.

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?

5. Aug 18, 2007

### 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 cant seam to think of how to get to where I want to be.
do you think you could start me off.

stu

6. Aug 18, 2007

### 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 cant see how to simplify the equation though, if you could start me off that would be great.

stu

7. Aug 18, 2007

### cristo

Staff Emeritus
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.

8. Aug 18, 2007

### 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