1. Aug 17, 2014

### killaI9BI

1. The problem statement, all variables and given/known data

Can you prove that vf2 = vi2 + 2aΔd?

2. Relevant equations

3. The attempt at a solution

I don't know where to start. I've not been given any values to use so I'm not sure how to go about answering the question.

Last edited by a moderator: Aug 26, 2014
2. Aug 17, 2014

### Staff: Mentor

What did your course cover so far?
This is just an application of energy conservation, but I don't know what you can use in such a proof.

3. Aug 17, 2014

### killaI9BI

This lesson is about acceleration. It's covered vectors and vector components, relative velocity and displacement so far.

4. Aug 17, 2014

### matineesuxxx

If you know any of the other kinematic equations then write them down and think about how you can eliminate time as a variable. are there any combinations or substitutions you can make given any of the other kinematic equations?

5. Aug 24, 2014

### killaI9BI

Maybe it'll help if I post the entire problem:

Derive an equation that relates vi, vf, Δd, and a. (Hint: Notice that Δt is not invloved.) Solve for Δt in the first equation. Substitute that value into Δt in the third equation. Solve for vf2. Can you prove that vf2 = vi2 + 2aΔd?

I think that this equation relates all of the variables that the problem is asking for:

vf = $\sqrt[]{}${vi2 + 2a X d}

There is a table on the page that the problem doesn't reference specifically but I'm now realizing that it must be relevant:

solve for Δt for the first equation:

Δt = (vf - vi) X a

Substitute that value into Δt for the third equation:
Δd = ((vi - vf)/2) X ((vf - vi) X a)

Solve for vf2:
vf2 = vi2 + 2a X d

I'm not sure if I did all of that correctly but it leaves me with the initial problem of proving that that vf2 = vi2 + 2aΔd

6. Aug 24, 2014

### matineesuxxx

What do you mean you still have to prove it? you started with true relations and ended up with the required equation; that's how this equation comes about. That's all you need to do.

7. Aug 24, 2014

### killaI9BI

My answer should then be yes I can prove that equation because..... ?

Like I said, I'm not sure I understand where to start with that.

8. Aug 24, 2014

### matineesuxxx

what you did is proof enough. In this sense derivation would be proof, because like I said, you are taking relations that are already known to be true, and ending up with the time independent kinematic equation.

9. Aug 25, 2014

### killaI9BI

I really do appreciate your input. I am pretty stunned when it comes to this stuff.....

I just don't understand how what I've done above is enough because as you can see here:

Proving that equation is the last problem. I have no idea how to answer it.

10. Aug 25, 2014

### Staff: Mentor

Rewrite the equation as $v_f^2-v_i^2=(v_f+v_i)(v_f-v_i)=2aΔd$

How is $(v_f-v_i)$ related to a and Δt?

How is $(v_f+v_i)$ related to the average velocity?

How is Δd related to the average velocity and Δt?

Chet

11. Aug 26, 2014

### matineesuxxx

Could this really be considered a proof? One could easily derive this relation through this method as well.

12. Aug 26, 2014

### Staff: Mentor

Who knows what they were thinking when they asked for a proof?????

Chet

13. Sep 12, 2014

### killaI9BI

lol thanks for your help guys!