what does area under the curve represent in physics

What if our force was not constant? these widths of the rectangles become infinitesimally small, Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. That means the area under 1 Answer Sorted by: 1 If you cover a distance x in time t, then, by definition, v = x t where v is your average velocity. George has always been passionate about physics and its ability to explain the fundamental workings of the universe. So what I mean is this. It means that the integral of a function (which, remember, is also the area under the curve) is equal to how much that function's anti derivative grew by over that range. George Jackson is the founder and lead contributor of Physics Network, a popular blog dedicated to exploring the fascinating world of physics. So the graph doesn't tail off to infinity? Temperature, kinetic theory, and the ideal gas law, [Wait, isn't the probability equal to zero for a gas molecule to be moving at any exact speed? Statement from SO: June 5, 2023 Moderator Action, Starting the Prompt Design Site: A New Home in our Stack Exchange Neighborhood. Subscribe Now:http://www.youtube.com/subscription_center?add_user=ehoweducationWatch More:http://www.youtube.com/ehoweducationThe area under a growth curve typically represents a very specific thing. underneath the curve, but for this first portion what do I do? where my force diminished continuously, and that's why Direct link to IsotonicFlaccidCell21's post area shows displacement/d, Posted 7 years ago. I just don't know what to do at all. What units describe the area under the curve? Why do microcontrollers always need external CAN tranceiver? If we made these rectangles is by using the work formula but another way to find the The area under a force-time graph is force multiplied by time, which is a quantity called impulse. How do precise garbage collectors find roots in the stack. So, in other words, for It's all of this area. It's also a triangle, so Why is area under curve derived using $y\,\mathrm dx$ instead of $y\,\mathrm dl\;?$, Displaying on-screen without being recordable by another app. Twice the size of Connecticut, about 12,000 square miles, Coast Guard officials said. Do NOT follow this link or you will be banned from the site! small rectangles to represent the area under any graph. tool to determine the work done for cases where the Proper way to solve this angular vs. linear speed calculation? So there's one more thing In other words the angle How fast can I make it work? I'm gonna show you an alternate US citizen, with a clean record, needs license for armored car with 3 inch cannon, Short story in which a scout on a colony ship learns there are no habitable worlds. It is used as a cumulative measurement of drug effect in pharmacokinetics and as a means to compare peaks in chromatography. The above approximation tells me that I can also do this by adding up approximations to the area of little slivers of the graph of $v$ as a function of $t$. did four joules of work. If. newtons, so I'll multiply by four newtons and then I get for that portion of the trip, I A crack, a defect in the hull materials or design or a structural failure could have imploded the Titan sub, experts told USA TODAY. The best answers are voted up and rise to the top, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. Does Pre-Print compromise anonymity for a later peer-review? Here's a look inside, Missing Titanic submersible: Maps, graphics show last location, depth and design, All five passengers on missing Titanic submersible dead after catastrophic implosion. of all of these rectangles added up, right, because to know that the work is equal to the area under a force graph? This is great. can find the area under my force graph, my force In the mid to late 1800s, James Clerk Maxwell and Ludwig Boltzmann figured out the answer to this question. In a gas, there are lots of molecules traveling at lots of different speeds. rev2023.6.28.43514. What is area under the curve of acceleration? If i gave you a graph of $v$ with respect to $t$ would you be able to tell me what the area under the curve represents without knowing (memorising) it? How do we find the work These cookies will be stored in your browser only with your consent. Encrypt different inputs with different keys to obtain the same output. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. Quantum computing is a , Spread the loveMany industries are searching for materials that combine strength, durability, and flexibility. average value) will not give us zero. That's basically just you How do you find the area under the curve with Z? It's just Fd cosine theta, The area under the curve is defined as the region bounded by the function we're working with, vertical lines representing the function's bounds, and the x -axis. done during that rectangular process and here's the really clever idea. - What is the difference? Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. I can do this, so this one's Calculating distance from acceleration is as easy as using this formula: D = v*t + 1/2*a*t^2. Click, MAT.CAL.300.5 (Area Under the Curve - Math Analysis), MAT.CAL.300.5 (Area Under the Curve - Calculus). start color #e84d39, start text, m, o, s, t, space, p, r, o, b, a, b, l, e, space, s, p, e, e, d, space, end text, v, start subscript, p, end subscript, end color #e84d39, start color #11accd, start text, a, v, e, r, a, g, e, space, s, p, e, e, d, space, end text, v, start subscript, a, v, g, end subscript, end color #11accd, start color #1fab54, start text, r, o, o, t, negative, m, e, a, n, negative, s, q, u, a, r, e, space, s, p, e, e, d, space, end text, v, start subscript, r, m, s, end subscript, end color #1fab54, v, start subscript, r, m, s, end subscript, equals, square root of, start fraction, 1, divided by, N, end fraction, left parenthesis, v, start subscript, 1, end subscript, squared, plus, v, start subscript, 2, end subscript, squared, plus, v, start subscript, 3, end subscript, squared, plus, point, point, point, right parenthesis, end square root, start color #e84d39, v, start subscript, p, end subscript, end color #e84d39, start color #11accd, v, start subscript, a, v, g, end subscript, end color #11accd, start color #1fab54, v, start subscript, r, m, s, end subscript, end color #1fab54, start color #e84d39, v, start subscript, p, end subscript, end color #e84d39, equals, 491, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction, 1100, start fraction, start text, m, i, end text, divided by, start text, h, r, end text, end fraction, right parenthesis, start color #11accd, v, start subscript, a, v, g, end subscript, end color #11accd, equals, 554, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction, 1240, start fraction, start text, m, i, end text, divided by, start text, h, r, end text, end fraction, right parenthesis, start color #1fab54, v, start subscript, r, m, s, end subscript, end color #1fab54, equals, 602, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction, 1350, start fraction, start text, m, i, end text, divided by, start text, h, r, end text, end fraction, right parenthesis. Impulse is equal to the change in momentum of an object. It's from this line that represents the force to the x-axis. So what is the interpretation behind each speed? Step 2: Look up your decimals from Step 1 in the z-table. could say the entire force times displacement times cosine theta. Question: In figure 3, what does the flat line at the beginning of the graph represent? Why? On Wednesday, one North Carolina-based HC-130 Hercules plane alone searched an area spanning 879 miles. Direct link to Shrimat Kapoor's post I understand all of this,, Lesson 1: Temperature, kinetic theory, and the ideal gas law. General Moderation Strike: Mathematics StackExchange moderators are Why is the area under a curve the integral? Maybe it's because you're a vegetarian, maybe you're already full, So, the formula of finding the area under the curve y is shown below: abf (x)dx. say I pushed with a whole bunch of constant forces but This website uses cookies to improve your experience while you navigate through the website. Direct link to overtakou's post So what is the interpreta, Posted 7 years ago. So there is a number of molecules at 600.000 m/s, and a number at 600.001 m/s, and a number at 600.002 m/s, and thus you get a continuous curve of number of molecules vs speed. The point is that in science and in real life, you come up against situations where you need to totalize or to aggregate or to accumulate some kind of growing quantity. 1/2 base times height. A remotely operated vehicle discovered the nose cone of the Titan submersible about 1,600 feet from the bow of the Titanic, authorities said. I've drawn the rectangle at the position $x$ on the $x$ axis so the height of the rectangle is $y(x)$. But remember that the bins are so thin that we actually refer to them just by the x-value (speed). This problem has been solved! in the direction of motion times the displacement or you It is just a , Posted 6 years ago. Can you see how these two things are equivalent? How can negative potential energy cause mass decrease? There are lots and lots of different graphs we could consider, but in all cases just think about the quantity $y\,dx$ and ask yourself what that quantity means. After performing this conversion, we have the following speeds: 1 m/s, 2 m/s, 3 m/s, 1 m/s, 2 m/s, and 3 m/s. Please help. No molecules are allowed to enter or exit, but the gas is cooled in a sealed container, Posted 8 years ago. Momentum is simply mass times velocity, while kinetic energy is one half of the product of the mass and the square of the velocity. but I'm not gonna do that. These 6 molecules have the following velocities, respectively: -1 m/s, -2 m/s, -3 m/s, +1 m/s, +2 m/s, and +3 m/s. a weaker and weaker force until your force became zero newtons. How did Boltzmann measure gas particle speed? I'll show you why. What does the area under the curve of a temperature-time graph represent? Direct link to Areeba's post You would take the integr, Posted 7 years ago. Making statements based on opinion; back them up with references or personal experience. determines the force down to this x-axis, if you find the area, that's gonna equal the work done. hamburger sitting right in front of you, but you don't want it. Direct link to ms15135iiserm's post yes when all the velocity, Posted 4 years ago. Jamie Frederick, the First Coast Guard District response coordinator, said Wednesday. you couldn't just use this, but now we derived this. We also use third-party cookies that help us analyze and understand how you use this website. know how to find the area of, like a rectangle or a This page will be removed in future. is gonna exactly equal the area under this triangle If we look at the right hand side of the above equation and determine the unit, we get, A = m/s s A = m/s s. A = meter A = meter. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. work done by that force and now we have a powerful Instead of just pushing How do I determine the time it takes to accelerate if I only know the distance traveled and what the amount of acceleration is? Why distance is area under velocity time line? Whenever you take cosine But remember that velocity is a vector and has a direction. As the graph shifts to the left, the height of the graph has to increase in order to maintain the same area under the curve. This is where quantum computing technology steps in. Learn how to do various types of science projects that will really help you get a better understanding of physics and science in general with help from a research scientist and one of the world's leading experts on star formation in this free video series. At a particular time along the graph, you're going to increase your position by a really really (infinitesimal) small amount, but that increase is going to be proportional to the height of the graph at that point. the force was varying the area underneath, it's Is a naval blockade considered a de jure or a de facto declaration of war? Chris Pilcher 11 years ago Since you are only looking at the magnitude of the velocity for the y-axis, couldn't you just call it the speed, since you only care (for the purpose of this example) about the scalar quantities that make up part of the velocity? The force is being applied in the direction of movement. We have a new and improved read on this topic. Share. Does "with a view" mean "with a beautiful view"? When search and rescue teams refer to "the water column," they mean in the water between the surface and the bottom. Why is it that th, Posted 7 years ago. the area of a triangle. but for the sake of just conceptually thinking about it, let's say you push with four These cookies ensure basic functionalities and security features of the website, anonymously. Statement from SO: June 5, 2023 Moderator Action, Starting the Prompt Design Site: A New Home in our Stack Exchange Neighborhood, Physics.SE remains a site by humans, for humans, relationship between kinematics and area under curve, How to prove the average velocity formula without calculus. Units of the derivative and finding unknown values. Chemistry . just get the area underneath. What is the formula for finding distance in physics? If it is possible to explain how I can find out, please explain simply, I am a just a high school student. So I'm gonna say that the ], [Show me equation for the Maxwell-Boltzmann distribution. Stack Exchange network consists of 182 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Work and the work-energy principle Work as the transfer of energy Work example problems Work as area under curve (In calculus, this is called finding the derivative.) So, positive four joules Now you might be like, alright, well, fat lot of good that does us, we can already find it with this formula. and your force was diminishing and you were pushing with It describes the distribution of speeds for relativistic particles. Can you legally have an (unloaded) black powder revolver in your carry-on luggage? Thanks for contributing an answer to Physics Stack Exchange! Best Answer If what you're trying to describe is a thermally isolated* system which is gradually heating up, and if your axes are temperature and time, then the total amount of heat $Q$produced after a given amount of time is related to the temperature $T$through the definition of heat capacity: $$Q(t)=C(T(t)-T_0)$$ Algebra Revise Video New Test 1 2 3 4 5 Estimating the area under a curve - Higher The area under a curve can be estimated by dividing it into triangles, rectangles and trapeziums. equation somewhat unusable but if the shape of the Let me just clear up any confusion. just plug the force in here, we could just plug the Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. so you're gonna push this hamburger to the right, If we're plotting speed on the x axis, is there then a maximum (the speed of light) the individual particles can't go beyond? What are the benefits of not using private military companies (PMCs) as China did? If i gave you a graph of v v with respect to t t would you be able to tell me what the area under the curve represents without knowing (memorising) it? Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Physics questions and answers. Work done is directly proportional to distance, hence as rectangles have a larger area, given that the time (length) and magnitude of speed/velocity (height) is the same, more work is done in the rectangular graph. therefor, causing negative displacement and ultimately negative work. varying force that the area underneath this graph is still The air molecules surrounding us are not all traveling at the same speed, even if the air is all at a single temperature. up the area of all these rectangles I get the work The graph above shows the area under the curve of the continuous function, f ( x). Keeping DNA sequence after changing FASTA header on command line. Ignoring friction and the mass of the spring, use energy methods to find (a) its maximum speed, and (b) its maximum stretch from equilibrium, in terms of the given quantities. underneath any force versus position graph is gonna equal the work, not just ones where the force is constant, even where the force is varying, if you can find the area Interference is one of the key principles that makes quantum , Spread the loveMany people suffer from high blood pressure, and it can be a serious problem if left untreated. Or is it possible to ensure the message was signed at the time that it says it was signed? Here you will estimate the area under a curve and interpret its meaning in context. How common are historical instances of mercenary armies reversing and attacking their employing country? Just above the section "What does the area under a Maxwell-Boltzmann distribution represent? Watch More: http://www.youtube.com/ehoweducation The area under a growth. infinitesimally small they would add up to the When you add up all those really really small sections you're adding up the heights under the graph at every time. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. How does "safely" function in "a daydream safely beyond human possibility"? Asking for help, clarification, or responding to other answers. In other words, power is the rate of doing work. An integral is a sum, so does not change the dimension. Learn more about Stack Overflow the company, and our products.
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