distance Definition and 48 Threads

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). Since spatial cognition is a rich source of conceptual metaphors in human thought, the term is also frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation (as exemplified by distance between people in a social network). Most such notions of distance, both physical and metaphorical, are formalized in mathematics using the notion of a metric space.
In the social sciences, distance can refer to a qualitative measurement of separation, such as social distance or psychological distance.

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  1. DaveC426913

    B How far away can a World So Newly Born Be at relativistic velocities?

    The premise (bear with me): In the year of '39 assembled here, the volunteers In the days when lands were few Here the ship sailed out into the blue and sunny morn Sweetest sight ever seen And the night followed day, and the storytellers say That the score brave souls inside For many a lonely...
  2. M

    B Formula for time in terms of acceleration and distance

    Reading Griffiths book on electromagnetics I stumbled upon his analogy to Newton and acceleration. Author claims that the formula for time when acceleration and distance are given is: $$t= \sqrt{\frac{2\lambda}{a}}$$, all is clear beside 2 in the nominator. My calculations goes as follows: $$a =...
  3. Agent Smith

    B Variation of Apparent Luminosity with Distance

    True luminosity of object X = ##T_X## Apparent luminosity object X = ##A_X## Distance of object X from observer = ##D_X## True luminosity of object Y = ##T_Y## Apparent luminosity of object Y = ##A_Y## Distance of object Y from observer = ##D_Y## Apparent luminosity is something measurable I...
  4. chwala

    Find the distance ##d## to a point in the given problem

    My problem is on how to arrive at ##d=\dfrac{mx-y}{\sqrt{1+m^2}}## My working steps are as follows; ##d^2=(x_1 - x)^2+ (y_1-y)^2## ##d^2=(\dfrac{y}{m} -x)^2+ (mx-y)^2## ##d^2=\dfrac{(mx-y)^2}{m^2} + (mx-y)^2## ##m^2d^2=(mx-y)^2(1+m^2)## ##d=\dfrac{mx-y\sqrt{1+m^2}}{m}## ...unless they...
  5. P

    I Distance between two light pulses

    If a source emits a light pulse then waited one second and sent another pulse does the distance between the two pulses remain constant ? If yes is that mean their relative speed is zero? But why when we use lorentz transformation their relative speeds gives us zero over zero but if they travel...
  6. S

    B Calculate distance between ends of a circle segment

    I was playing with a small piece of rope I had on the table, moved it to a curve - circle segment - and figured I wanted to calculate the distance between ends of the curve - and failed. Now I'm confused and embarrassed. Here is what I did: The rope has length L. I put the ends of the rope on a...
  7. paulb203

    Locus of all points -- Imprecise question?

    TL;DR Summary: When asked to show the LOCUS OF ALL POINTS how precise should the questioner be? I was asked to draw THE LOCUS OF ALL POINTS 3cm from a line. I measured 3cm above and below the line, and drew two parallel lines there. Then drew two semi-circles with radii 3cm out from either...
  8. yashraj

    I Do electromagnetic waves fade with distance in vacuum?

    I want to know that when a charged particle accelerates then the electromagnetic wave so produced will loose it's strength or can say fades with distance or not ? If yes then what happens to its frequency and also tell me if electromagnetic waves fades away with increasing distance from the...
  9. B

    Studying Best recognized distance learning options in mathematics?

    I am a physics major in the second year and always have loved maths. Now that interest has grown into something bigger and I am thinking of taking some recognized distance courses in mathematics so that I will have something to show in case I decide to do a masters in mathematics. It will be...
  10. NikolasLund

    Minimal distance between two planes moving perpendicularly

    This problem is from Prof. Jaan Kalda's study guide to the IPHO. The problem can be solved by optimization, but there is apparently also a geometric approach, which is the one Kalda suggests. Initially I, being naive, tried to solve the problem by calculating the resulting distance the red plane...
  11. A

    I Instantaneous velocity - displacement and distance

    Instantaneous velocity is defined as the first derivative of displacement with respect to time: ##\vec{v} = \dfrac{d \vec{r}}{dt}## However, instantaneous velocity is also defined as the first derivative of function of distance with respect to time: ##v = \dfrac{ds}{dt}## Why do these two...
  12. I_Try_Math

    Determining impulse given stopping distance and change in velocity

    I think I was able to work out that ## F=-346.2m ## and that ## t= .087 sec## but maybe I'm wrong. Without knowing the mass, I'm not sure how I can find the impulse. Any hints or corrections are appreciated.
  13. N

    How far do acorns drift in the wind?

    this one is our extra credit problem with no instructions. just creative thinking.
  14. chwala

    What distance will be covered before coming to stop?

    Phew; back n forth on this anyway, my lines ... ##v_{1} = \dfrac{1000}{20} = 50## m/s in the first ##10## seconds. ##v_{2} = \dfrac{1000}{30} = \dfrac{100}{3} ##m/s in the first ##35## seconds. where ##v_1## and ##v_2## are the respective velocities in ##10s## and ##35s## respectively...
  15. putongren

    Two Trains and a Bee: Distance Question

    This is a question from the MIT Open courseware website. (1). d = vt + ut let t = time it takes d = (u + v)t t = d / (u + v) (2). d = vt + ut d - vt = ut. Substitute t with d / (u + v) d - v*(d/(u+v)) = u*(d/(u+v)) d - v*(d/(u+v)) = “distance...
  16. putongren

    Bees and Trains: A distance problem

    This question is from the MIT Courseware. I’m having difficulty finding the general equation to solve the problem (1). d = vt + ut d = (u + v)t t = d/(u + v) (2). d = vt + ut d - vt = ut sub t with d/(u+v) d - (v*d)/(u+v) = (u*d)/(u+v) I’m done with the...
  17. M

    Simultaneous events separated by distance and time

    For this problem, Does anybody please know how events can be separated by time in one frame and distance in another? This notation does not seem physically correct to me. Thanks!
  18. R

    B Speed is distance multiplied by time -- Is this correct?

    Hello, In this study https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9784821/, the distance the punch travelled from start to impact is 0.49 meters and the time taken from start of punch (that's it, they define the start of punch as the moment the elbow first start to extend) to impact is 0.1...
  19. felizgu

    How Far Can A Person See?

    The tallest building in the world is Burj Khalifa in Dubai, United Arab Emirates, at 2717 feet and 160 floors.The observation deck is 1450 feet above ground level. How far can a person standing on the observation deck see (with the aid of a telescope)? Use 3960 miles for the radius of Earth...
  20. felizgu

    Number of Miles In One Light Year

    TL;DR Summary: This is an astronomy application. One light-year is defined by astronomers to be the distance that a beam of light will travel in 1 year (365 days). If the speed of light is 186,000 miles per second, how many miles are in a light-year? Express your answer in scientific notation...
  21. barryj

    Determining the sound level of a leaf blower

    I have a leaf blower that states the sound level is 75dB. My question is, at what distance is this measured. It seems that as you get closer to the source, the dB number will increase drastically. If I double the distance from the source, then the power should go down by a factor of four or 6...
  22. brotherbobby

    Launch service between two stations along a flowing river

    Attempt : I start by compying and pasting the problem as it appeared in the text. Please note that for reasons of clarity, I replaced landing station ##\text{K}## with station ##\text{N}##. Let me draw a picture of the problem situation. The landing stations M and N are shown in red and the...
  23. Earthworm69

    I Would moving the mouths of a wormhole affect the internal distance?

    Lets say I formed a traversible wormhole with one mouth on each end of my garage. If I picked up one of the ends and drove it to the park, would the distance inside the wormhole increase or otherwise be effected as well? This is my first post on physics forums - Hi everybody...
  24. Jim Alexandridis

    Kinematics problem from a competition: Will the 2 sliding boxes collide?

    The distance covered by the first box is :s1max=v²/2|a|=v²/2μg where a=-μg by second newtons law Similarly S2max=(2v)²/2|a|=4v²/2μg It gas to be s1max+s2max≥S => v²/2a +4v²/2a ≥s => 5v²≥2aS =>v²≥ 2μgS/5=> v≥√(2μgs/5) But this is in the possible solution, am I wrong somewhere? I appreciate your help
  25. wirefree

    I Is there a way to calculate this transformation?

    Namaste & G'day! Imagine a helicopter view of a Polo ground. It's length & breadth are known. Now you are seated where the blue dot is. Your view is such: How do mathematicians calculate the distance travelled by a ball from the second perspective? From the top view, this would be...
  26. Ben S

    I How Does Distance to Proxima Centauri Affect Simultaneous Events?

    Referring to this statement: "Proxima Centauri is approximately four light-years away. For any particular event on Earth, there is an eight-year span of events on Proxima Centauri that could count as simultaneous with it, depending on your reference frame." How does the distance between Earth...
  27. I_Try_Math

    Max distance a truck can travel without box falling off

    The equation at the bottom is me attempting to solve for the distance. Without knowing the mass of the box and truck my approach to this problem isn't possible?
  28. brotherbobby

    Distance-time graph of a ball throw vertically up from a fixed point

    Statement of the problem : I copy and paste the statement of the problem to the right as it appeared on the website. Given below is the graph of the ball as its distance from a fixed point with time. Attempt : Where does this fixed point, say ##\text{P}## lie? Imagine the fixed point lied...
  29. srnixo

    Measuring the Velocity of Sound in this Lab Exercise

    Here is the exercise: Which one seems logical and correct ? this one: [ Normally when we increase distances, the velocity of sound decreases?] Or this one? You might wonder why. Well, my friend in class told me that the second table could be correct because the experiment was conducted at...
  30. F

    I Looking for the most suitable distance for binary clustering

    Hello everyone. I have a pandas dataset in python which has n+1 columns and t rows. The first column is a timestamp that goes second by second during a time interval, and the other columns are the names of the people who log in the server. The t rows of the other columns indicate if the person...
  31. F

    I Reported uncertainties for time and distance in physics experiment

    Hello, I was looking at my physics lab manual... There is a table reporting time and distance data which were both measured and collected (see below). My understanding is that the uncertainty for different and measured time instants should be the same because the time was measured with the same...
  32. D

    Stargazing What is the maximum distance that parallax error can be used?

    using the Earths orbit, what is the maximum distance that can be measured using parallax error?
  33. James Pryor

    Writing: Input Wanted Distance between the star systems Sirius and Alpha Centauri?

    Need the distance between the two star systems (Sirius & Centauri) for a science fiction novel.
  34. M

    B How to calculate Aphelion distance?

    Is it possible to calculate the Aphelion distance, - when I only know the Perihelion distance and perihelion speed ?
  35. brslagle

    Distance traveled when decreasing velocity

    dont know where to start. Other than it will take 5 seconds for v = 0m/s
  36. James1019

    Projectile motion when only given distance and acceleration

    TL;DR Summary: Find horizontal velocity? I have no idea how to solve the problem, the question only provide distance 16cm(h),3.6cm(v) and acceleration = 0
  37. chwala

    Show that acceleration varies as cube of the distance given

    In my approach i have distance as ##(x)## and velocity as ##(x^{'})##, then, ##(x^{'}) = kx^2## where ##k## is a constant, then acceleration is given by, ##(x^{''}) = 2k(x) (x^{'})## ##(x^{''}) = 2k(x)(kx^2) ## ##(x^{''}) = 2k^2x^3##. Correct?
  38. Astro-Eddie

    B Where does the 1/2 in 1/2 at^2 come from?

    I am currently studying Newton's laws and mechanics. I have this question: Why is distance=half a*t^2? Where did the 1/2 come from? Can someone explain this without using calculus?
  39. G

    I How does an object know how far to move when it's moving?

    Space must have properties, it's not just empty nothing, and one of those properties is distance. When an object moves through space at a velocity V information has to be transferred between the object and space. The object has the information that it is moving at velocity V which is...
  40. feynmansorange

    Verifying the acceleration of gravity in our lab (help with error please)

    Data and graphs here (the time is measured every 1/30 of a second, but for some reason, Google Sheets thought 1/30 wasn't a number so its in decimals!!! very confusing!!! so sorry about that!). why is the slope only 4.68, should it not be 9.81m/s^2? is the slope of m/s^2 not supposed to be...
  41. Ggb

    B Coulumb's Law at 1 light year distance

    Hi, What happens to the force when the particle are kept at 1 light year distance. I agree practically the force would be very weak because of inverse square law, theoretically what happens to the force?
  42. D

    I Inverse Square Law for Black Holes

    When you are calculating the gravitational force between two masses and one of them is a black hole, do you still use the distance to the center of mass as you would in Newtonian gravity to find the force? Or is the distance measured only to the event horizon? Is the inverse square law modified...
  43. golya

    Relating acceleration to distance and time

    I’m an absolute beginner and I need someone to show me where I’m wrong. Knowing the formula of acceleration ∆v (change in velocity) / ∆t (change in time) where ∆v = ∆x (distance) / ∆t, a common way of relating acceleration to distance is to say a (acceleration) = (distance/time)/time =...
  44. G

    I How exactly does spooky action at a distance violate SRT?

    Hi. It's often stated (for example in Wikipedia) that spooky action at a distance would violate SRT. But how, exactly? As far as I understand, SRT does neither assume nor predict that the speed of light is an upper limit (it even allows for hypothetical tachyons, but that's not the point). I...
  45. Mordred

    I James Webb telescope calibration

    I understand that many of the extreme distance objects were incorrectly calibrated for their distance and subsequent age. I have been trying to track down the related articles detailing the error with the applicable mathematics. If anyone knows where I can get the related calibration papers it...
  46. Slimy0233

    Calculate Distance Traveled: Instantaneous vs. Average Velocity

    edit: I don't know why my latex isn't rendering, any help would be appreciated. Edit 2: The question was due to a misunderstanding I had, I thought integrating instantaneous velocity would give me average velocity. I have attached what I have tried so far. I had a doubt. Can you calculate the...
  47. flamebane

    I know everything to do on this problem except one thing

    Even though I have all the formulas needed to do this problem, I cant figure out how to get rA, rB and rA' aswell as rB'
  48. I

    What Does d Represent in Interatomic Spacing Diagrams?

    according to the figure, it's look like d is the distance between the center of two adjacent atoms, and so it should be simply L. I don't understand what d represents in the figure. that's the solution: Even if d is half the distance between two adjacent atoms that positioned diagonally (I...
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