# Finding Final Velocity

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?

Hootenanny
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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?
Do you know any SUVAT equations?

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.

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

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

Isn't it displacement/time?

Hootenanny
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Isn't it displacement/time?
That would give you the average velocity - you want the average acceleration.

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

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

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.

Hootenanny
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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.
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".

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?"

Hootenanny
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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?"
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.

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

Hootenanny
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Yes, but I don't know the final velocity in that equation.
I know, that's what you're trying to find out - you know everything except the final velocity.

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 ????

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

The average is 5.87.

Hootenanny
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The average is 5.87.
So, if the average is 5.87 and the initial is zero. Can you use this:
$$v_\text{ave} = \frac{v_\text{final}+v_\text{initial}}{2}$$
to work out the final velocity?

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

Hootenanny
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Why is the bottom 2? Why isn't it 1.875
I have two numbers: 5 and 10. What is their average (or mean)?

I know that, but earlier you said that average velocity = change in distance/change in time. Now it's (final velocity - initial velocity)/2?

My time was 1.875 s

Hootenanny
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I know that, but earlier you said that average velocity = change in distance/change in time. Now it's (final velocity - initial velocity)/2?
Both are correct. To work out the average velocity you can take the total distance travelled and divide it by the time taken. Alternatively, you can treat the initial and final velocities as numbers and simply find their average by adding them together and then dividing by two.

This is the essence of the problem. You need to use both definition of average velocity.

Well just to make sure, I got 11.74 as a final velocity. Is this correct for the equation:
5.87 = (x-0)/1.875

Hootenanny
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Well just to make sure, I got 11.74 as a final velocity.
That is almost correct. It should be 11.73 in/s. You likely rounded to early in your calculation.

How about the change in speed as it rolled from one end of the book to the other?

Is the change 11.73 since it started at 0 and ended up at 11.73 m/s?