What is One dimensional: Definition and 145 Discussions

In physics and mathematics, a sequence of n numbers can specify a location in n-dimensional space. When n = 1, the set of all such locations is called a one-dimensional space. An example of a one-dimensional space is the number line, where the position of each point on it can be described by a single number.In algebraic geometry there are several structures that are technically one-dimensional spaces but referred to in other terms. A field k is a one-dimensional vector space over itself. Similarly, the projective line over k is a one-dimensional space. In particular, if k = ℂ, the complex numbers, then the complex projective line P1(ℂ) is one-dimensional with respect to ℂ, even though it is also known as the Riemann sphere.
More generally, a ring is a length-one module over itself. Similarly, the projective line over a ring is a one-dimensional space over the ring. In case the ring is an algebra over a field, these spaces are one-dimensional with respect to the algebra, even if the algebra is of higher dimensionality.

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  1. N

    Electric field on a one dimensional line

    Homework Statement An electric charge Q has been evenly divided over a line with the length L. Calculate the electric field in the field spot X0. X0 > L Homework Equations The Attempt at a Solution E = 0SL(dQ/(4*pi*E0*X0^2)) 0SL = the integral over 0 to L >_< dQ = Q*dx/L...
  2. Z

    Physics question about deriving a one dimensional kinematic equation?

    Okay, we all know that ΔX = ViT + 1/2AT^2 Say I drop a stone from rest and I want to find its distance at a given time knowing the acceleration. Since the initial velocity is zero and its accelerating vertically we can say. ΔY = 1/2AT^2 ΔY = (AT^2) / 2 <------------------------- Keep in mind...
  3. D

    Particle in a one dimensional box: probability of observing px between p and dp

    Homework Statement Show that for a particle in a one dimensional box of length L, the probability of observing a value of p_x (recall \hat{p}_x is Hermitian and that \Psi is not an eigenfunction of \hat{p}_x) between p and dp is: \frac{4|N|^2 s^2}{L(s^2-b^2)^2}[1-(-1)^n \cos(bL)]dp where...
  4. M

    What Is the Minimum Strength of a Fishing Line to Stop a Drifting Salmon?

    1. The tension at which a fishing line snaps is commonly called the line's “strength.” What minimum strength is needed for a line that is to stop a salmon of weight 87 N in 11 cm if the fish is initially drifting horizontally at 3.3 m/s? Assume a constant deceleration. 2. F=ma, W=mg 3. I...
  5. M

    One dimensional motion in Halliday Resnick Fundamentals

    Hi this problem is one I couldn't understand very well so I couldn't do big attempts at solving Homework Statement since I have it on pdf and I don't want to mistake in typing and that there is a picture in it I made the problem into a picture...
  6. T

    How Do You Calculate Acceleration and Distance in One Dimensional Motion?

    Homework Statement A car accelerates uniformly from rest to a speed of 40 mi/h in 12.0 secs find A) the distance the car traveled during this time and B) the constant accelaration of the car Homework Equations a) Displacement of an object as a function of time: delta x =1/2(v0+v)T B)...
  7. Advent

    One dimensional mechanical system.

    Homework Statement Given the dynamical system \dot{x}=1-x^2, show that F(x,t)=\frac{1+x}{1-x}e^{-2t} is a constant of that system, and obtain the general solution of the differential equation with F(x,t) Homework Equations Above The Attempt at a Solution As F(x,t) is a...
  8. F

    One Dimensional Hot Air Balloon Kinematics

    Homework Statement A hot-air balloon has just lifted off and is rising at the constant rate of 2.3 m/s. Suddenly one of the passengers realizes she has left her camera on the ground. A friend picks it up and tosses it straight upward with an initial speed of 12 m/s. If the passenger is 2.5m...
  9. C

    One dimensional motion problems

    Homework Statement 1) Runner A is initially 4.0 mi west of a flagpole and is running with a constant velocity of 6.0 mi/h due east. Runner B is initially 3.0 mi east of the flagpole and is running with a constant velocity of 5.0 mi/h due west. How far are the runners from the flagpole when...
  10. P

    One Dimensional Baseball Kinematics

    Homework Statement 52. A baseball player catches a ball 3.1 s after throwing it vertically upward. With what speed did he thow it, and what height did it reach? Homework Equations def of a = t^-1 (V - Vo) The Attempt at a Solution t = (3.1 s)2^-1 = 1.55 s def of a = t^-1 (V -...
  11. P

    How Fast Does a Baseball Accelerate During Pitching Motion?

    Homework Statement A baseball pticher throws a baseball with a speed of 44 m/s. Estimate the average acceleration of the ball drugin the trowing motion. It is observed that in throwing the baseball, the pitcher accelerates the ball through a dsiplacement of about 3.5 m, from behind the body...
  12. P

    Finding Launch Velocity and Maximum Height of a Toy Rocket Passing by a Window

    Homework Statement A toy rocket passes by a 2.0 m-high window whose sill is 10.0 m above the ground. The rocket takes .15 s to travel the 2.0 m height of the window. What was the launch speed of the rocket, and how high will it go? Assume the propeltant is burned very quickly at blastoff...
  13. C

    One dimensional motion problem, overcoming head start

    I know this problem has been posted before, but I think my answer is correct and I want to know why it was considered wrong! Homework Statement Cars A and B are racing each other along the same straight road in the following manner: Car A has a head start and is a distance Da beyond the...
  14. P

    Another One Dimensional Motion Problem

    Homework Statement A rock is thrown vertically upward with a speed of 12.0 s^-1 m. Exactly 1.00 s later, a ball is thrown up vertically along the same path with a speed of 20.0 s^-1 m. (a) At what time will they strike each other? (b) At what height will the collision occur...
  15. P

    Easy One Dimensional Kinematics

    Homework Statement A rcok is dropped from a sea cliff and the sound of it striking the ocean is heard 3.4 s later. If the speeds of sound is 340 s^-1 m how high is the cliff. Homework Equations X = Xo + Vo t + 2^-1 a t^2 The Attempt at a Solution Ok 340 average velocity and sense...
  16. P

    How Long to Accelerate for Desired Time?

    Homework Statement A runner hopes to complet the 10,000 m run in less than 30.0 min. After running at constant speed for exactly 27.0 min, there are still 1100 m to go. The runner must tehn acceelerate at .20 s^2 m for how many seconds in order to achieve teh desired time? Homework...
  17. S

    Specific heat of solid of one dimensional quartic oscillators

    Homework Statement A system consists of N very weakly interacting particles at temperature T sufficiently high so that classical stat mech is applicable. Each particle has mass M and is free to perform one dimensional oscillations about its equilibrium position. Calculate the heat capacity...
  18. A

    One dimensional motion problem

    Homework Statement Challenge Problem(2.96) from University Physics textbook: In the vertical jump, an athlete starts from a crouch and jumps upward to reach as high as possible. Even the best athletes spend little more than 1.00s in the air (their "hang time"). Treat the athlete as a particle...
  19. Phrak

    Do one dimensional vectors have a sign?

    Do one dimensional vectors have a sign? (:devil:)
  20. K

    How Fast Must the Race Car Go in the Last 2 Laps to Qualify?

    Homework Statement "A race car driver must average 180 km/h for 4 laps to qualify for a race. Because of engine trouble, the car averages only 150 km/h over the first 2 laps. What speed must be maintained for the last 2 laps?" Homework Equations v= d/t The Attempt at a Solution i...
  21. C

    One dimensional transient heat flow of a hoop

    1. Problem: derive the energy balance from first principles of a hoop of inner radius ri, outer radius ro. the hoop material has a density of rho (p), heat capacity of c and thermal conductivity k. the center of the hoop has a temperature of T1 and the gas inside the hoop has a convection...
  22. T

    One Dimensional Kinematics: Force

    Homework Statement A .3 kg ball is compressed a maximum of 0.6 cm when it strikes the floor at 9.29 m/s. Assuming acceleration is constant, what is the force the ball exerts on the floor? Homework Equations vf^2 = v0^2 + 2A(x-x0) Once I find A it will be easy, since F=MA The...
  23. L

    Why Is the Density of States Formula Applicable in a 1D Quantum Wire?

    I have seen, in several places, derivations of a formula for the current flow in a 1d quantum wire connected to electron reservoirs at its respective terminals. All of these derivations at some point invoke the formula for the number of states per unit volume of a 1d quantum "box," n(k) dk = (2...
  24. K

    Curvilinear One Dimensional System

    Homework Statement There is a child's toy, which has the shape of a cylinder mounted on top of a hemisphere (the picture the book has looks like a half of a circle with a square on top.). The radius of the hemisphere is R and the CM of the whole toy is at a height h about the floor. (this in...
  25. P

    Deriving equation to describe lattice vibrations of a one dimensional crystal

    When setting up this derivation one assumes a chain of identical atoms. The interatomic interaction between atoms is short ranged and so only affects neighbouring atoms (see Hook and Hall, "Solid State Physics" chapter 2.3.1). The potential V(r) is expanded as a taylor series about r = a to...
  26. M

    Entropy of a One Dimensional Polymer

    Homework Statement Polymers are made of very long molecules, usually tangled up in a configuration that has lots of entropy. As a very crude model of a rubber band, consider a chain of N links, each of length l. Imagine that each link has only two possible states, pointing either left or...
  27. D

    One Dimensional Kinematics of Object

    Homework Statement An object is released from rest at a height h. It travels 0.31h during the first second of its descent. Determine the average velocity of the object during its entire descent. Homework Equations X - Xo = Vot + .5at^2 v^2 = Vo^2 + 2a(X - Xo) X - Xo = .5(Vo + V)t...
  28. Y

    Possible webpage title: What Remains Constant in One-Dimensional Kinematics?

    The area under both curves (velocity vs time) from t =0 to t =tf is the same. Which of the following quantities is the same from t =0 to t = tf? A. average position B. average velocity C.average accerleration D. total displacement E. jerk( the derivative of accerleration. THE...
  29. M

    Normal Modes - One Dimensional Oscillating Systems

    Hi Can someone help me with the following questions please (see attachment)? I really need some help on the following: i). Drawing a force diagram for each particle (I really hate drawing these). As a guess for m1, am I right in thinking that H and N point up and W points down? But...
  30. K

    One dimensional infinite potential well problem

    hi, I am not getting idea to solve below problem A particle of mass m is in a one-dimensional ,rectangular potential well for which V(x)=0 for 0<x< L and V(x)=infinite elsewhere. The particle is intially prepared in the ground state ψ1 with eigen energy E1. Then , at time t=0, the potential...
  31. X

    One dimensional lattice dispersion relation

    I'm doing an experiment, in which I have a one dimensional lattice held up by strings. That is I have a series of n masses each of mass M each connected to each other by springs with spring constant C and unstretched length a. Each mass is suspended from the ceiling by a string of length L. I'm...
  32. F

    One Dimensional Kinematics Jet Problem

    Homework Statement A Boeing 747 "Jumbo Jet" has a length of 59.7 m. The runway on which the plane lands intersects another runway. The width of the intersection is 29.9 m. The plane decelerates through the intersection at a rate of 6.33 m/s2 and clears it with a final speed of 42.3 m/s. How...
  33. F

    Find the one dimensional particle motion in a given potential

    I'm not looking for a solution, but rather trying to understand the question. We've been given a series of potentials, U(x), and have been told to find the one-dimensional particle motion in them. For example: U(x) = V(tan^2(cx)), V>0 My initial reaction was just to solve it for x(t)...
  34. M

    How Does a Particle's Motion Change Direction and Velocity Over Time?

    a particle moves along the x-axis. its position is given by the equation x=2+3t-4t^2 determine its position when it changes direction. and its velocity when it returns to the position it had at t=0
  35. P

    Quantum vaccum one dimensional?

    Hello. Is a quantum vacuum 1 dimensional? Thanks.
  36. N

    One Dimensional Diffusion Equation

    Homework Statement Solve: \frac{\partial u}{\partial t} = k\frac{\partial^2 u}{\partial x^2}, 0<x<\pi, t>0 with initial condition u(x,0)=f(x)=\left\{\begin{array}{cc} 1,& 0\leq x< \pi/2 \\ 0, &\pi/2 \leq x < \pi \end{array}\right and with non-homogeneous boundary conditions...
  37. B

    Number of Positive Solutions for Omega?

    Could someone help me out on the following questions? Q. Consider the free vibrations of a string of length L clamped at x = 0 and constrained at x = L such that u_x \left( {L,t} \right) = - ku\left( {L,t} \right),k > 0. (a) Show that the eigenvalues are given by the positive roots of...
  38. D

    One dimensional motion problem =/

    Hey everyone, Well, I am sort of stuck on this problem: Two trains, one traveling at 78 km/h and the other at 135 km/h, are headed toward one another along a straight, level track. When they are 980 m apart, each engineer sees the other's train and applies the brakes. The brakes decelerate...
  39. Amith2006

    What Force Keeps a Body Moving at Constant Velocity on a Horizontal Surface?

    Sir, Please say whether these 2 problems are right. 1) A body of mass 2kg moving on a horizontal surface with an initial velocity of 4 m/sec comes to rest after 2 seconds. If one wants to keep this moving on the same surface with same velocity, what is the force that is needed to be...
  40. M

    One dimensional motion with friction

    Hello, I was wondering if someone could help me out with this one. Its been years since I've done physics and this problems is bugging the hell out of me. Thanks
  41. A

    Need help with one dimensional kinematics problem

    Hello, I've been working on the following problem for quite some time, with no success: A commuter train travels between two downtown stations. Because the stations are only 1.15 km apart, the train never reaches its maximum possible cruising speed. The engineer minimizes the time t between...
  42. I

    How far does the police car travel to overtake the speeding car?

    A car traveling @ 120 km/h passes by a parked police car. If it takes 5 seconds to start the police car, which then accelerates @ 3 m/s^2 to a maximum speed of 150 km/h, how far does the police car travel in overtaking the speeding car, which maintains a speed of 120 km/h? The 5 seconds is...
  43. S

    One dimensional motion magnitude

    An object is moving in a straight line with a constant acceleration. Its position is measured at three different times, as shown in the table below. Time (s) | Position, (m) 56.40 | 9.700 58.20 | 19.042 60.00 | 38.428 Calculate the magnitude of the acceleration at t=58.20 s I am not...
  44. T

    Exploring Single Dimension Objects: Understanding and Describing Them"

    I do not understand and cannot comprehend anything existing in a single dimension. I have heard briefly that strings exist in a single dimension. How would you describe a single dimension? I understand 3 dimensions, length- height-depth. But wouldn't a single dimension object be invisible in...
  45. P

    One dimensional motion of a tortoise

    can anyone help me with this problem please-- A tortoise can run with a speed of 0.10 m/s and a hare can run 20 times as fast. in a race they both start at the same time but the hare stops to rest for 2.0 minutes. the tortoise wins by 20 cm. how long does the race take? what is the...
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