# Question on theory for solving 2015 AP Physics C Free Response Questions

• RoboNerd
In summary, the conversation discusses the free response questions and solutions for the AP Physics C Mechanics exam from 2015. The conversation delves into the explanation of the solutions for questions 1e and 3c, including why the velocity squared is plotted on the y-axis and why the point on the graph for question 1e is before tf/2. The conversation also covers the relationship between distance traveled and features of the velocity-time graph.
RoboNerd

## Homework Statement

Here are the free response questions:[/B]
https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap15_frq_physics_c-m.pdf

Here are the solutions:
https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap15_physics_cm_sg.pdf

I do not understand how they solved a few of the questions

more below

## The Attempt at a Solution

So for 1. e.
Why do they have the difference in slopes of the two line segments with the the first segment being steeper than the second? And why is the point before tf/2 and not at tf/2?
In other words... what is the explanation behind the way they drew the graph the way they did?

And then for 3. (c)
Why do they choose to have velocity squared for the y-axis and the length for the horizontal axis?
I see how the units of the slope of the line match the acceleration... but I do not understand the theory that allows g to be calculated from it. Could anyone please explain?

For your second question as to why they are plotting velocity squared on the y-axis and length on the horizontal axis. Taking the equation derived in part 3 (b) ##v=\sqrt{3gL}## and squaring it we obtain ##v^2=3gL##, now note that ##3g## is a constant and ##L## is the independent variable. Therefore as ##L## increases linearly it is being multiplied by ##3g##. Perhaps it's easier to see if you write the equation as ##v^2=(3g)L##.

Ex: Suppose ##L## increases from 0 to 1, then you will have ##v^2(1)=(3g)(1)=3g## and ##v^2(0)=(3g)(0)=0##, your slope is then ##m=\frac{3g-0}{1}=3g##

Yes! I see now! Thanks so much.

Could ypu please take a look at my question regarding 1e? Thanks a lot!

RoboNerd said:
Yes! I see now! Thanks so much.

Could ypu please take a look at my question regarding 1e? Thanks a lot!
What two forces act on the block? Does each have a component parallel to the slope?
When the block is going up the slope, do those two components act in the same direction or in opposite directions?
What about when going down the slope?
Which case will produce the greater net force?

Forces acting: friction and gravity. Both have such components.

When block is going up the slope, they act in the same direction.
When block is going down, they act in opposite direction.

Going up the slope will produce a greater magnitude of net force... ... so that is why the segment of the velocity vs time is steeper... more acceleration.

Yes?

If I got this right, then I do not understand why the point is before tf/2

RoboNerd said:
Forces acting: friction and gravity. Both have such components.

When block is going up the slope, they act in the same direction.
When block is going down, they act in opposite direction.

Going up the slope will produce a greater magnitude of net force... ... so that is why the segment of the velocity vs time is steeper... more acceleration.

Yes?

If I got this right, then I do not understand why the point is before tf/2
That's all correct.
What do you know about distance traveled and features of the velocity-time graph?

OK. so my distance traveled equals integral of velocity time graph.

Velocity y axis. time x axis.

OK... so how does that factor in the solution with the point being before tf/2?

RoboNerd said:
OK. so my distance traveled equals integral of velocity time graph.

Velocity y axis. time x axis.

OK... so how does that factor in the solution with the point being before tf/2?
you know the graph will look like two lines of different slopes, so the areas will be two triangles. What can you say about the relationship between those two areas?

These areas must be the same since distance covered is the same.

RoboNerd said:
These areas must be the same since distance covered is the same.
Right. But the slopes are different, and both triangles are based on the x-axis. So what does that tell you about the lengths of those bases?

Well... I will need to have a larger base for the second triangle... it will take less time for me to reach the top going up than the bottom going down.

So thus, the point is less than tf/2.

Thanks a lot for the help!

RoboNerd said:
So thus, the point is less than tf/2.

Thanks a lot for the help!
You are welcome.

## 1. What is the best approach to solving the 2015 AP Physics C Free Response Questions?

The best approach to solving these questions is to carefully read and understand the given scenario and identify the relevant theories and principles that apply. Then, use problem-solving strategies such as drawing diagrams, writing equations, and breaking the problem into smaller parts to solve for the desired quantities.

## 2. How important is it to show all of my work in the solutions?

It is essential to show all of your work in the solutions for these questions, as it demonstrates your understanding of the concepts and the steps you took to arrive at the final answer. Partial credit may be awarded for correct work, even if the final answer is not correct.

## 3. Can I use my calculator for these questions?

Yes, you can use a calculator for these questions. However, it is crucial to understand when and how to use your calculator to solve the problem effectively. Some questions may require you to show your work without the use of a calculator.

## 4. Are there any specific formulas or equations that I should memorize?

While there are some fundamental formulas and equations that you should be familiar with, it is more important to understand the underlying concepts and how to apply them. It is always good to have a general understanding of the equations and their significance, but you can also refer to a formula sheet during the exam.

## 5. How can I prepare for the 2015 AP Physics C Free Response Questions?

You can prepare for these questions by practicing with previous years' exams and reviewing the relevant concepts and theories. It is also helpful to work on problems with a study group or seek guidance from a teacher or tutor if needed. Additionally, make sure to manage your time well during the exam and carefully read and understand each question before attempting to solve it.

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