What is One-dimensional motion: Definition and 14 Discussions
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.
In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space.
The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur in mathematics and the sciences. They may be parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in.
Homework Statement
A particle of mass m moves along the x–axis under the influence of force ##F_x=-ax+bx^3## , where a and b are known positive constants.
(a) Find, and sketch, the particle's potential energy, taking U(0) = 0
(b) Identify and classify all equilibrium points
(c) Find the...
Homework Statement
A projectile is fired horizontally from a height of 20 meters above the ground, with an initial velocity of
7.0 m/s. How far does the projectile travel horizontally before it reaches the ground?
Homework Equations
X=VoT+1/2AT^2
The Attempt at a Solution
I solved for time...
Homework Statement
A rock is released from rest from the top of a very high cliff, and accelerates downward at g.
Approximately how far does the rock travel in the first 7 seconds of its free-fall? (Assume no air friction.)
Homework Equations
X=Xo+VoT+1/2AT^2
The Attempt at a Solution
I...
Homework Statement
Q.[/B] A body dropped from a height H above the ground strikes an inclined plane at a height h above the ground. As a result of the impact, the velocity of the body becomes horizontal. The body will take the maximum time to reach the ground if :
(a) ##h=\frac H4## (b)...
I am not good at typing out formulas and equations on the internet, so I took pictures of what I did instead. I hope that's not too informal.
1. Homework Statement
A rock is tossed straight up with a velocity of 19 m/s. When it returns it fell into a 10 m deep hole.
Q: What is the rock's...
Here's the question:
Three particles A, B and C are situated at the vertices of an equilateral triangle ABC of side d at time t = 0. Each of the particles moves with constant speed v. The particle at A always has its velocity along AB, B along BC and C along CA. At what time will the particles...
Hi, this is my first time posting on this forum. This is a question about how to approach questions about one-dimensional motion with drag.
A link to the question:
http://puu.sh/5fOCO.png
While attempting this question, I thought the two equations they were referring to were:
dy/dt = v...
I'm having a little trouble with the wording in this problem. (And this isn't the first time).
My instructions are:
"Draw a pictorial representation of each situation described below. That is, (i) sketch the situation, showing appropriate points in the motion, (ii) establish a...
Homework Statement
A red car and a green car, identical except for the
color, move toward each other in adjacent lanes and parallel to an x
axis. At time t 0, the red car is at xr 0 and the green car is at xg
220 m. If the red car has a constant velocity of 20 km/h, the cars pass
each other...
Homework Statement
A falling object travels one-fourth of its total distance in the last second of its fall. From what height was it dropped?
Homework Equations
equations of motion for constant acceleration
Thanks in advance !
A truck covers 40.0 m in 8.50 s while smoothly slowing down to a final velocity of 2.80 m/s
a. Find the truck's original speed.
b. Find its acceleration
a) I'm using x=1/2(vo+v)t to find the original velocity but I keep getting vo=12.21m/s (the books answer is 6.61m/s)
b) For the...
Homework Statement
The accelration of a marble in a certain fluid is proportional to the speed of the marble squared and given (in SI units) by a=-3.00v2 for v>0. If the marble enters this fluid with a speed of 1.50 m/s, how long will it take before the marble's speed is reduced to half of its...
Homework Statement
A stone is dropped from a height (h) and falls the last half of its distance in 4 seconds.
(a) What is the total time of the fall?
(b) From what height was the stone dropped?
Homework Equations
h=1/2(g)(T)²
The Attempt at a Solution
T=√2(T-4)
Homework Statement
36 g bullet, speed of 350 m/s strikes a 8 cm fence post. It is retarded by an average Force is 3.6 x 10^{6} N while going through the post.
a. Speed of bullet when it emerges?
b. How many boards could the bullet penetrate?
Homework Equations...