# Finding Final Velocity

1. Sep 12, 2011

### BuhRock

1. I am doing an experiment. I am rolling a ball down textbook that is propped up on one side. If the ball rolled 11 inches in 1.875 seconds. How can I get the final velocity and the change in velocity?

2. I know I can get the average velocity by dividing 11/1.875 and the initial velocity is 0 isn't it?

3. TI know I can get the average velocity by dividing 11/1.875 and the initial velocity is 0 isn't it? So how can I get the final and the change?

2. Sep 12, 2011

### Hootenanny

Staff Emeritus
Do you know any SUVAT equations?

3. Sep 12, 2011

### BuhRock

No, I don't. I have read over chapter 1, but there isn't anything to do with velocity in there. It's all just unit conversions, significant numbers, scientific notation, and that stuff.

4. Sep 12, 2011

### Hootenanny

Staff Emeritus
Okay. Do you know how to work out the [average] acceleration?

5. Sep 12, 2011

### BuhRock

Isn't it displacement/time?

6. Sep 12, 2011

### Hootenanny

Staff Emeritus
That would give you the average velocity - you want the average acceleration.

7. Sep 12, 2011

### BuhRock

I knew that lol, I meant change in velocity/change in time.

8. Sep 12, 2011

### Hootenanny

Staff Emeritus
Yes! That is correct.

Thinking about this again, this problem is going to be difficult if you haven't met SUVAT equations before. Are you sure that you have never seen any of these: https://www.physicsforums.com/showpost.php?p=905663&postcount=2 before?

9. Sep 12, 2011

### BuhRock

Yes, I'm sure. This is my third week in this distance learning physics class. So far we haven't covered acceleration yet, just velocity.

10. Sep 12, 2011

### Hootenanny

Staff Emeritus
Do you have any other information, such as the height of the slope?

I would highly recommend reading the second on 1D Kinematics in your textbook, it may also be called "uniform acceleration" or "constant acceleration".

11. Sep 12, 2011

### BuhRock

The height of the slope doesn't matter apparently. I sent in a question to my instructor on how to go about this and he replied with this:

"From that timing you can determine the ball's average velocity on the ramp. Knowing that it started from rest, with velocity zero, you can infer a final velocity.

The final velocity averaged with the initial velocity should be the average velocity. Knowing the average and initial velocities, how do you then infer a final velocity? In other words, what velocity would you average with 0 to get your average velocity?"

12. Sep 12, 2011

### Hootenanny

Staff Emeritus
Indeed you can infer the final velocity from the information you have. However, textbook usually intend for you to use kinematic equations for such questions, that was why I was pushing you that way. Now that I know your tutor doesn't want you to use SUVAT equations, we can move forward.

The average velocity is simply

$$v_\text{ave} = \frac{v_\text{final}+v_\text{initial}}{2}$$

The ball starts from rest, so your initial velocity is zero as you correctly say. Therefore, you should be able to compute the final velocity using the above equation.

Last edited: Sep 12, 2011
13. Sep 12, 2011

### BuhRock

Yes, but I don't know the final velocity in that equation.

14. Sep 12, 2011

### Hootenanny

Staff Emeritus
I know, that's what you're trying to find out - you know everything except the final velocity.

15. Sep 12, 2011

### BuhRock

I'm not trying to just get the answer here, but I really don't know how to get it. I know that:

a = (vf - vi)/t

and

Vf=Vi+a(t)

I'm not sure how to get the Vf without acceleration. On the other hand, I can't get acceleration because it asks for vf in the equation. I'm not sure if I'm supposed to switch it around.

a = (x-0)/1.875 ????

16. Sep 12, 2011

### Hootenanny

Staff Emeritus
You don't need the acceleration, only the average velocity.

17. Sep 12, 2011

### BuhRock

The average is 5.87.

18. Sep 12, 2011

### Hootenanny

Staff Emeritus
So, if the average is 5.87 and the initial is zero. Can you use this:
to work out the final velocity?

19. Sep 12, 2011

### BuhRock

Why is the bottom 2? Why isn't it 1.875

20. Sep 12, 2011

### Hootenanny

Staff Emeritus
I have two numbers: 5 and 10. What is their average (or mean)?