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.
Imagine this question in 2 dimensions, time (t) and distance (x), that is (t,x). Alice (A) is at the origin, x=0. Bob (B) begins at x=c. Thus we have A(0,0) and B(0,c). Both Alice and Bob send a light signal towards the other but let's say the signal changes colour every second by the colours of...
Hi,
if I have a equation like (just a random eq.) p_dot = S(omega)*p. where p = [x, y, z] is the original states, omega = [p, q, r] and S - skew symmetric.
How does the equation appear if i only want a system to have the state z? do I get z_dot = -q*x + p*y. Or is the symmetric not valid so I...
Summary: Integrating the 1 dimensional MB Distribution in terms of translational kinetic energy up to infinity, does not yield ##\frac{1}{2}k_BT## as it should be.
The format for the 3 dimensional Maxwell-Boltzmann Distribution is ##A\cdot e^{-\frac{E}{k_BT}} \cdot g(E)## in which ##A## can be...
Homework Statement
Suppose a particle moves along the x-axis beginning at 0. It moves one integer step to the left or right with equal probability. What is the pdf of its position after four steps?
2. Homework Equations
Binomial distribution
##P(k) = {{n}\choose{k}} p^k (1-p)^{n-k}##
The...
Homework Statement
Identify the motion that the different sections of the graph describe
Homework EquationsThe Attempt at a Solution
t=0-2 is accelerating
t=2-4 is stationary
t=4-5 accelerating
t=5-9 decelerating/slowing down
Options which are given: Constant speed, moving back to the...
Homework Statement
A particle with mass m and electric charge e is confined to move in one dimension along the x -axis. It experiences the following potential: V(x) = infinity when x<0, V(x) = -e^2/4*pi*ε*x when x≥0
For the region x ≥ 0 , by substituting in the Schrödinger equation, show that...
The ground state wave-function of a 1-D harmonic oscillator is
$$
\psi(x) = \sqrt\frac{a}{\sqrt\pi} * exp(-\frac{a^2*x^2}{2}\frac{i\omega t}{2}).
$$
a) find Average potential energy ?
$$
\overline{V} = \frac{1}{2} \mu\omega^2\overline{x^2}
$$
b) find Average kinetic energy ?
$$
\overline{T} =...
Homework Statement
- A Dragster at the starting line accelerates at 8 m/s^2 to the finish line. If it took 4.6 s, how long is the track?
- The Dragster deccelerated to a stop in 100m. How long did it take?Homework Equations
x = 0 + 1/2at^2
The Attempt at a Solution
The first part of the...
Homework Statement
I'm trying to find the point at which FG attracting to the moon = FG attracting to the earth...
5.98e24 kg = Earth Mass
7.35e22 kg = Moon Mass
3.84e8 m = Distance from Earth to Moon
Deductions...
a = 3.84e8 - b
b = 3.84e8 - a
a+b = 3.84e8
Homework Equations
g = G m / r2...
Homework Statement
During a car accident, a vehicle with an intial velocity of 100km/h hits a concrete wall. The "crumple zone" in the front of the vehicle is a space that makes up the engine compartment
that is designed to allow the passenger compartment to continue forward a distance of...
a car starts from rest travels for 5.0s with a uniform acceleration of + 1.5m/s^2. The driver then applies the brakes, causing uniform acceleration of -2.0m/s^2. If the brakes are applies for 3.0s (a) how fast is the car going atthe end of the braking period and b how far has it gone
I have...
A race driver has made a pit stop to refuel. After refueling, he starts from rest and leaves the pit area with an acceleration whose magnitude is 5.5 m/s^2; after 4.1 seconds he enters the main speedway. At the same instant, another car on the speedway and traveling at a constant velocity of...
Alright, I have wondered this for a very long time and probably thought about it for longer than I should have but the more I think about it, the more I seem to be correct and the more frustrating it is to talk to people about it...
Anyways, I'm sure everyone has heard of the saying "lefty...
Homework Statement
Here is the problem verbatim (values have been slightly changed, also assume a frictionless environment):
"A 4.3 kg block A and 6.0 kg block are connected by a string of negligable mass. Force FA = (15 N) acts on block A; force FB = (24 N) acts on block B. What is...
Homework Statement
A car accelerates at 2.10 m/s2 along a straight road. It passes two marks that are 29.6 m apart at times t=4.10 s and t=4.90 s. What was the car's velocity at t=0?
I'm assuming the car has constant acceleration of 2.10 m/s2
Given
\Deltax = 29.6 m
a = 2.10 m/s2
vi = ...
Homework Statement
1. A particle of mass m is constrained to move along a straight line. In a certain
region of motion near x = 0 , the force acting on the particle is F = -F_0 sin(bx) , where F_0 and b are positive constants.
(a) Find the potential energy of the particle in this region...
Homework Statement
A box slides along a surface with a positive initial velocity. It the experiences an acceleration of -0.25m/s^2. After traveling 4.00 meters, its velocity is +0.50m/s. How long did it take for the boxto travel the 4.00 meters?
Homework Equations
\Deltax=Vot + 1/2 a t^2...
Homework Statement
A runner hopes to compleate the 10,000m run in less than 30.0min. After running at a constant speed for exactly 27.0min there are still 1100m to go. The runner must then accelerate at 0.20 m/s^2 for how many seconds in order to achieve the desired time.
*note* person does...
Homework Statement
Two cars C and D travel in the same direction on a long, straight section of a highway. During a particular time interval \Deltat0, car D is ahead of car C and speeding up while car C is slowing down.
During the interval \Deltat0, it is observed that C gains on car D...
Homework Statement
(1) A speed trap is set up with two pressure activated strips placed across a highway, 116 meters apart. A car is speeding along at 29.6 meters per second, while the speed limit is only 19.4 meters per second. At the instant the car activates the first strip, the driver...
Hello! Could you please check for errors in the following HW problems?
Thank you!
A. Homework Statement
A rolling ball moves from x1=3.4 cm to x2=-4.2 cm during the time from t1=3.0 s to t2=6.1 s. What is the average velocity?
Homework Equations and The Attempt at a Solution
Average...
Hi, having trouble with the following problem:
A stone is thrown vertically upward from a bridge 30.0m high at an initial velocity of 15.0 m/s . How long will it take for the stone to hit water?
I set it up first by writing my givens down:
initial velocity = 15.0 m/s.
distance (x)...
The driver of a car wishes to pass a truck that is traveling at a constant speed of 19.0 m/s. Initially, the car is also traveling at a speed 19.0 m/s and its front bumper is a distance 23.7 m behind the truck's rear bumper. The car begins accelerating at a constant acceleration 0.550 m/s^2...
You are driving your new sports car at a velocity of 90km/hr, when you suddenly see a dog step into the road 50m ahead. You hit the brakes hard to get maximum deceleration of 7.5m/s^2. How far will you go before stopping? Can you avoid hitting the dog?
I got 540m, which I know is wrong. V=0...
:confused: :confused: Help! I need to know how to work this problem! A motorcyclist moving with an initial velocity of 8.0 m/s undergoes a constant acceleration for 3.0s, at which time his velocity is 17.0 m/s. What is the acceleration, and how far does he travel in the 3.0 s interval?
I have a Homework here I'm trying to solve like the last 3-4 hours but somehow I'm stuck so I ask you guys for help:
They gave me the Green Function like this:
http://idefix.physik.uni-freiburg.de/~aufgabe/THEO204/theo9/img50.png
with...
On a frictionless horizontal air table, puck A (with mass 0.366 kg) is moving toward puck B (with mass 0.254 kg ), which is initially at rest. After the collision, puck A has velocity 0.119 m/s to the left, and puck B has velocity 0.655 m/s to the right.
What was the speed of puck A...
Hello, I'm having a bit of trouble starting this problem:
A ball is dropped from a height of 30 m. At the same instant another ball is thrown straight up from the ground with aspeed of 30 m/s. How long are the balls in the air before they reach the same height?
I'm not sure what equation...
Ok, how can we see a point (0 dimensions) or a line (1 dimension) without it being 2 dimensional as well, and how can something exist within a 2 dimensional plain if dimensionality doesn’t explain something to exist. How can 3 dimensions exist if dimensionality must be infinite at any point in...