What is Initial: Definition and 1000 Discussions

In a written or published work, an initial or drop cap is a letter at the beginning of a word, a chapter, or a paragraph that is larger than the rest of the text. The word is derived from the Latin initialis, which means standing at the beginning. An initial is often several lines in height and in older boscene are known as "inhabited" initials. Certain important initials, such as the Beatus initial or "B" of Beatus vir... at the opening of Psalm 1 at the start of a vulgate Latin. These specific initials, in an illuminated manuscript, were also called initiumsIn the present, the word initial commonly refers to the first letter of any word or name, the latter normally capitalized in English usage and is generally that of a first given name or a middle one or ones.

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  1. M

    Car-Truck Collision: Initial Common Velocity

    Homework Statement A car with a mass of 1400 kg is westbound at 50 km/h. It collides at an intersection with a northbound truck having a mass of 2000 kg and traveling at 40 km/h. What is the initial common velocity of the car and truck immediately after the collision if they have an...
  2. Destroxia

    2nd Order Homogeneous, Real Roots, Initial Value

    Homework Statement Solve the initial value problem Homework Equations Quadratic Formula The Attempt at a Solution My problem is that I don't understand how to solve the constants now, I understand, 2 equations, 2 unknowns, but when I plug the y(0) = 0 into the YsubH equation...
  3. Math Amateur

    MHB Category Theory - Initial and Final Objects

    I am reading Paolo Aluffi's book, Algebra: Chapter 0. I am currently focused on Chapter I, Section 5: Universal Properties. I need some help Example 5.3 and Exercise 5.2 in this section. QUESTION 1Example 5.3 reads as follows: Can someone clearly explain why \emptyset is initial ... We...
  4. Math Amateur

    MHB Initial Objects in the Category Ring

    I am reading Paolo Aluffi's book, Algebra: Chapter 0. I have a question related to Aluffi's description of initial objects in the category ring ... ... In Chapter III, Section 2. on the category ring, we read the following: QUESTION 1 In the above text, we read the following: " ... ... This...
  5. I

    Initial and final velocity from a sheared casting

    Good evening all, I am looking for a little guidance with relation to trying to find the initial and impact velocity of a section of a steel casting if it shears. Given the results of stress analysis, the mass of the sheared section would be 200kg maximum. The input force at that would be...
  6. P

    Questions on Newton's Method: Investigating Convergence & Initial Guesses

    I have three questions regarding Newton's method. https://en.m.wikipedia.org/wiki/Newton-Raphson#Failure_of_the_method_to_converge_to_the_root According to this wikipedia article, "if the first derivative is not well behaved in the neighborhood of a particular root, the method may overshoot, and...
  7. R

    How To Find Initial Angular Velocity

    Homework Statement The angle of a pendulum is θ(t)=(0.270rad)cos(4.00t+1.00π), where t is in seconds. Determine the initial angular velocity. Homework Equations ω=2πf The Attempt at a Solution [/B] I solved for the frequency, which was 6.37E-1 Hz and subbed it into the formula above and...
  8. S

    Calculating Initial Decay Rate of Ga-67 Isotope

    Homework Statement An initially pure 3.4 g sample of Ga-67, an isotope with a half life of 78 hr. What is its initial decay rate? Note: Molar Mass values given in tables for chemical elements are for natural mix isotopic ratios. (i.e. the relative percentages of each isotope normally present...
  9. shanepitts

    Why same initial value in power series

    Homework Statement Find a power series representation for the function below & determine the radius of convergence. f (x)=(1+x)/(1-x)2 2.Relevant equation Shown in attached image below which is the solution the problem. 3.The attempt at a solution I'm trying to fathom the solution here...
  10. M

    MHB Initial Value Problem for a System of Linear Differential Equations

    Hey! :o We have the following initial value problem: $$x' = \frac{1}{2}(45 − x) + \frac{1}{4}(y − x) \\ y' = \frac{1}{4}(x − y) + \frac{1}{2}(35 − y) + \frac{1}{2}(z − y) + 20 \\ z' = \frac{1}{2}(y − z) + \frac{1}{2}(35 − z)$$ This can be written as follows: $$\begin{pmatrix} x\\ y\\...
  11. Zafa Pi

    Sensitivity to initial conditions

    Let M = {x1, x2, x3, ...} U {p} be a perfect metric space. Let f be continuous, taking M to M with f(xn) = xn+1 and f(p) = p. I would like to know if this dynamical system is necessarily sensitive to initial conditions.
  12. N

    Initial velocity for a leaping cat

    Homework Statement Hello, usually when solving basic velocity problems, if the object starts from rest, then its initial velocity would be 0. But why is it that, if a cat were to leap from rest, its initial velocity wouldn't be 0, but something else? My friend told me about muscle...
  13. C

    Calculating initial velocity using kinematic equations

    Hi! I'm working on a problem for class and am having trouble figuring out how to calculate the initial velocity, which I need in order to calculate acceleration and from there the value of an unknown force. I thought I was on the right track, but my professor reminded me that I need to use the...
  14. D

    Initial acceleration problem: Two children on a frictionless floor

    Homework Statement A girl of the mass 30kg and a boy of the mass 45kg sit on a frictionless floor holding two ends of a rope. The boy pulls on the rope. The girl moves towards the boy with an initial acceleration of 3ms^-2. The boy A. Moves towards the girl with an initial greater acceleration...
  15. D

    Finding the horizontal range without initial velocity

    Homework Statement A locust jumps at an angle of 43.8 degrees and lands 1.0 m from where it jumped. If it jumps with the same initial speed at an angle of 62.4 degrees, how far would it jump then? X-component knowns: Initial velocity = v(cos(43.8)) displacement = 1m angle = 43.8 degrees...
  16. Glenboro

    What is the initial momentum of the sled-person system?

    1. Homework Statement A 75.0 kg person runs at 3.00 m/s and jumps onto a sled of mass 10.0 kg already moving in the same direction as the person at 2.00 m/s. a) What is the initial momentum of the sled-person system? b) What will the final momentum of the sled and the person be? c) What is the...
  17. cnh1995

    How does voltage signal travel through multiple capacitors in an RC circuit?

    Suppose we have an RC series dc circuit with two capacitors C1 and C2 and resistance R. If the switch is closed at t=0, all the voltage appears across R initially. Fine.. But how does it reach across R through two insulation barriers (breaks) in the circuit? I can understand the mechanism for...
  18. Y

    Initial and Final Energy problem

    Homework Statement [/B] A 2.4 kg piece of wood slides on the surface shown in the figure . The curved sides are perfectly smooth, but the rough horizontal bottom is 31m long and has a kinetic friction coefficient of 0.27 with the wood. The piece of wood starts from rest 4.0m above the rough...
  19. cnh1995

    How does an inductor determine the applied voltage in an RL circuit?

    If the switch in an RL dc circuit is closed at t=0, the current i in the inductor rises exponentially. But at t=0, i=0 because the inductor generates a back emf equal to the applied voltage at t=0. So in absence of any current,how does the inductor come to know that the switch has been closed...
  20. M

    MHB Initial & Boundary Value Problem-Fourier

    Hey! :o We have the initial and boundary value problem $$u_{xx}(x,y)+u_{yy}(x,y)=0 , x^2+y^2<1 \\ u(x,y)=0 \\ u(1, \theta)=\sin{\theta}, 0< \theta< \pi$$ $$U_{\rho \rho}(\rho, \theta)+ \frac{1}{\rho^2} U_{\theta \theta}=0, 0< \rho<1, 0< \theta< \pi$$ We are looking for solutions of the form...
  21. R

    Calculating Initial Energy of a Spring-Connected Mass

    Homework Statement A block of mass m = 0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching half the distance (x/2) from equilibrium position, it hits another block and comes to...
  22. gracy

    Wedge and block initial momentum

    Homework Statement :block slides on smooth triangular wedge kept on smooth floor.Find velocity of wedge when block reaches bottom. (image is attached) Homework Equations :Let the velocity of the triangular wedge be V.And v be the velocity of block m. [/B] applying conservation of linear...
  23. J

    What makes these initial functions so special?

    People say that if you could break a function down into these three functions (constant, successor, projection or sometimes called initial/basic functions) using some operators, then it is primitive recursive. What makes these three functions so special?
  24. S

    Initial Tension Of Parallel Spring System

    Homework Statement How to calculate initial tension or pretension in a system of two parallel springs. F=5.33213N K1+K2=53.0597 x=0.095 Individual springs have initial tension of 0.25N so I would expect an answer of 0.5N but I can't get there. Homework Equations F=(k1+k2)x The Attempt at a...
  25. K

    Find Initial value such that solutions go to -infinity

    Homework Statement For the equation y=-4e^t -4/3-2t+Ce^(3t/2), find the initial value y(0)=y_0 that separates solutions that grow positively as t -> infinity from those that grow negatively. Homework Equations (All are given in the problem statement.) The Attempt at a Solution I have half...
  26. S

    Phase Difference with Initial Conditions for SHM

    Homework Statement A mass-spring system with a natural frequency of 3.6 Hz is started in motion with an initial displacement from equilibrium of 6.1 cm and an initial velocity of 0.7 m/s. What is the value of ϕ? (Question aside: Finding the amplitude of the resulting function?) Homework...
  27. V

    Projectile motion, finding initial speed

    An object fired at an angle of 30° above the horizontal takes 2.5 s to travel the last 12 m of its vertical distance and the last 10 m of its horizontal distance. With what speed was the object launched? (Note: This problem does not stipulate that the initial and final elevation of the object...
  28. J

    Fortran Problem with initial state in FORTRAN

    I have created an initial state code with perodic boundary conditions and normal distribution of velocities. I not know where is the problem, when I compile the computer detect the 112 error. Could anyone help me please? Thanks! the code is...
  29. S

    The Initial Reaction of a Voltaic Cell

    I just want to start by saying that I have found many questions very similar to this one using the search bar, but I still don't understand exactly what happens initially in a simple voltaic cell with a salt bridge (Daniel cell). For example, I am trying to figure out what initially happens in...
  30. R

    2nd Law of Thermo relation to initial condition of universe

    While reading some articles on Wikipedia I came upon one interesting statement that essential says (I've rephrased for clarity; correct me if I'm wrong): "The Time-asymmetry of the second law of thermodynamics is due to the initial conditions of our universe" Can someone elaborate on what...
  31. C

    Finding initial velocity of a projectile

    Homework Statement A football is kicked at an angle of 60 degrees to the horizontal and travels a distance "R" before hitting the ground A.) find the initial speed of the football Homework EquationsThe Attempt at a Solution : [/B] I would presume I would need to find initial velocity of X...
  32. M

    Initial development of set theory and determinism in QM

    I am considering the following question and I want you to agree (but perhaps you don’t):Rutherford wrote a letter to Bohr, as an answer to a previous letter from Bohr containing one of the first of Bohr’s descriptions of the atomic model, saying that he understood the atom model Bohr advocated...
  33. K

    Mathematica Mathematica NDSolve initial condition

    Hi, I am trying to use NDSolve in Mathematica to solve a set of differential-algebraic equations: NDSolve[{-6250 f[t] + 0.025 p[t]^2 f[t] + 0.1 f[t]^3 + 3 q[t] f'[t] + f''[t] == 0, 1.5230870989335428*^-35 p[t]^4 + q'[t] == 0, -4.32*^36 q[t]^2 + 10/3 \[Pi]^2 p[t]^4 + 0.0125 p[t]^2...
  34. tjae

    Find the initial velocity of truck before collision

    Question: A car of mass 1500kg collides head-on with a truck of mass 9000kg. After the collision, the wreckage is at rest. The speed of the car just before the collision was 30m/s. What was the speed of the truck just before the collision? Relevant Equation(s): m1v1+m2v2 = m1v1'+m2v2' (?) My...
  35. W

    Finding the initial velocity and time period of a projectile

    Homework Statement In the Fig. What should be the initial velocity (magnitude and direction) of the arrow? Also calculate the time of flight. Homework EquationsThe Attempt at a Solution I have formulated 2 equations: v*cos(theta) * t = 20 and 3 = (v * Sin(theta) * t) + (9.81 * t^2)/2 when...
  36. J

    Solve the ODE with initial condition:

    y''-10y'+25=0 Solve the ODE with initial condition: y(0) = 0, y' (1) = 12e^5 . I keep getting y=12/5e^5x when c1=0 and c2=12/5 ... but Answer key says y=2xe^5x what am I doing wrong?
  37. M

    Projectile motion- solve for initial velocity

    Homework Statement A ball is thrown upward at an angle of 30degrees to the horizontal and lands on the top edge of a building that is 20m away. The top edge is 5.0m above the throwing point. How fast was the ball thrown? Homework Equations x=v0t+(1/2)at2 vf2=V02+2ax vx=v0cosθ vy=v0sinθ The...
  38. evinda

    MHB Solving Initial Value Problem: Determine Solution $y$

    Hi! (Smile) Consider the initial value problem $$\left\{\begin{matrix} y'(t)=\sqrt{|y|}, 0 \leq t \leq 2\\ y(0)=1 \end{matrix}\right. \tag 1$$ Show that for this problem the assumptions of the following theorem hold: "Let $c>0$ and $f \in C([a,b] \times [y_0-c, y_0+c])$. If $f$ satisfies at...
  39. A

    Simple Harmonic Motion, Initial Displacement vs Initial Cond

    Hi everybody, I'm writing an exploration on the mathematics of simple harmonic motion and I stumbled across something I fail to understand in one of my resources (http://tutorial.math.lamar.edu/Classes/DE/Vibrations.aspx). In the example the author uses toward the end of the resource, the...
  40. Meagan

    Find the car's initial speed

    Homework Statement A 5000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in the figure below. Both springs are described by Hooke's law and have spring constants with k1 = 1700 N/m and k2 = 3000 N/m...
  41. A

    Initial velocity by measuring negative acceleration?

    Hi, Quick Qustion : If an object is propelled through the air (e.g. a ball is thrown), once the ball has left the throwers hand it will immediatly start to have negative acceleration (at least in the x plane). If the negative acceleration is measured at the same point in time after the ball...
  42. H

    Solving initial velocity for falling object

    Homework Statement A stone is dropped from a bridge that is 65 m high. A second stone is thrown downwards 2 seconds later. Both the stones are heard hitting the water at the same time. The speed of sound is a constant 343 m/s. What is the initial velocity of the second stone. Homework...
  43. Coffee_

    Classical field theory, initial and boundary conditions

    Hello, I am taking an introductory class on non relativistic classical field theory and right now we are doing the more mathematical aspect of things right now. The types of differential equations in the function ##f(\vec{r},t)## that are considered in this course are linear in the following...
  44. Q

    How to find initial velocity without being given time

    Homework Statement a projectile is launched at an angle of 26.5 above the horizontal at a height of 1.11m. the range is 2.331m. find the initial velocity and time given that acceleration due to gravity is 9.8m/s^2. The Attempt at a Solution first, I split the velocity into its components...
  45. V

    Finding Initial Velocity with Given Distance and Angle?

    Hello, All! The following problem wasn't assigned to me, it was used for last semesters physics class at my college. However, I feel it is interesting enough and I can't seem to find the correct answer. A ball is launched from the top of a 28-m high vertical cliff at an angle of 31° . Ignoring...
  46. Calpalned

    Dropping a package with initial velocity

    Homework Statement A helicopter is ascending vertically with a speed of 5.30m/s . At a height of 100m above the Earth, a package is dropped from a window. How much time does it take for the package to reach the ground? [Hint: v0 for the package equals the speed of the helicopter.] Homework...
  47. B

    Determine initial conditions of the capacitor's Vc and inductor's Il at t=0

    Homework Statement Given the following circuit: [/B] Where R=C=L=1, with Vs(t) = sin(wt) and complete response Vo(t)=A*sin(wt + π/4). Homework Equations Determine the init. cond. of the capacitor voltage Vc and Inductor current Ic at t = 0. Also, find A and w.[/B]The Attempt at a Solution...
  48. R

    Motion between two charged surfaces, find initial speed

    Homework Statement Two charged, parallel, flat conducting surfaces are spaced d = 1.3 cm apart and produce a potential difference ΔV = 625 V between them. An electron is projected from one surface directly toward the second. What is the initial speed of the electron if its comes to rest just at...
  49. E

    Material Model: initial conditions of equation?

    Hello guys, actually I'am working on a model to describe the creep-behaviour of a concrete specimen. This model is based on a 'generalized maxwell-chain'. I attached a picture, where you can see it: The acting load is the tension \sigma, while E_0 and E_1 are the stiffnesses of the...
  50. P

    Calculating the Initial Kinetic Energy & Momentum of a Truck

    Homework Statement A truck is initially moving at velocity v. The driver presses the brake in order to slow the truck to a stop. The brake applies a constant force F to the truck. The truck rolls a distance x before coming to a stop, and the time it takes to stop is t. 8. Which of the following...
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