Velocity Definition and 1000 Threads

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction of motion (e.g. 60 km/h to the north). Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.
Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object has a changing velocity and is said to be undergoing an acceleration.

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  1. B

    Engineering Velocity Ratio, mechanical advantage, Efficiency of a screw jack

    Hello, I have completed the question below. I am just unsure on whether i am correct or not. I am unsure on Mechanical Advantage. As i have seen a few different equations. Question: Answer: a) Velocity Ratio = $$\frac{\text{Distance Moved By Effort}}{\text{Distance Moved By Load}}$$...
  2. F

    Finding Velocity of Car Slowing Down: v_0-c*(t-t_1)^2/2

    At time t=0 , a car moving along the + x -axis passes through x=0 with a constant velocity of magnitude v0 . At some time later, t1 , it starts to slow down. The acceleration of the car as a function of time is given by: a(t)= 0 0≤t≤t1 -c(t−t1) t1<t2 where c is a positive constants in...
  3. T

    Heisenberg and Varying the Velocity

    Good Morning When we derive the Euler Lagrange equations using Hamilton's Principle, we make a point of varying the velocity and the position at the same time, (despite the fact that, normally, they are related through a derivative). I do understand that this is allowed: we are trying to find...
  4. RemotePhysics

    Require help with angular velocity and people flying off the planet

    My solutions (attempts) : a> w=v/r | r=6.35x10^6m | therefore V=7.04x10^-5 m/s b> speed of rotation is faster at the equator than the pole as w=v/r. As w remains constant, as r increases towards the pole V has to decrease. c> F = W - R d> Stuck here. I presume that I have to use the equation...
  5. aspodkfpo

    How Does Resolving Angular Velocity into Components Affect Its Magnitude?

    Angular velocity is the degrees by which something rotates over a time period. If I have an angular velocity in one direction and I resolve it into its components, its components would obviously be of lesser value. Here's what I don't get. When I imagine this scenario, I see that the thing...
  6. G

    To find the relative velocity of the wind as seen from a car

    Could I please ask for any help with the following question: Here's my attempt: (i and j are unit vectors in the directions of east and north respectively) (apologies that LaTeX is simply not working for me, I'll label the angles in each case T and P as shown in my diagram) Let the...
  7. G

    Mechanics: Angular Velocity Vector Questions

    Answers are the following : (i) v=(2cost)i - (2sint)j -(1/2)k (ii)2.06m/s (iii)2m/s^2 horizontally towards the vertical axis, making an angle of pi/4 with both the I and j axes.
  8. jeffrey

    Pulley angular velocity problem

    Further given: - every beam is infinite stiff - pulleys are massless - cables don't stretch, no slip, and frictionless. -Every pulley has a diameter D except pulley Q. Pulley Q has diameter 0.5*D So what I don't understand is how to calculate/determine the velocity at R and S. Can someone help...
  9. Sunny Huang

    A How to calculate the interband velocity matrix in a graphene system

    In graphene system, the velocity operator sometimes is v= ∂H/ħ∂p, and its matrix element is calculated as <ψ|v|ψ>, i.e., v_x = v_F cos(θ) and v_y = v_F sin(θ) [the results are the same with Eq. 25] for intraband velocity. Recently, I see a new way to calculate the velocity matrix (Mikhailov...
  10. D

    DV Calculation clarification (rocket booster)

    When calculating the dV available from a rocket booster, the below calculation is used: (ISP . g) . ln(Mass when full/Mass when empty) Is 'g' always equal to 9.81 in this equation, or do you use the actual gravitational acceleration that the booster will experience, at it's given altitude, to...
  11. S

    I Differential form of the velocity equation in a non-standard configuration

    I'm reading a text on special relativity (Core Principles of Special and General Relativity), in which we start with the equation for composition of velocities in non-standard configuration. Frame ##S'## velocity w.r.t. ##S## is ##\vec v##, and the velocity of some particle in ##S'## is ##\vec...
  12. D

    Triangle calculation for the resultant velocity

    Top example- How do I get to 31.7 m/s from 30.8 and 7.7? This is way over my head and need help. Thanks in advance Dean
  13. Rongeet Banerjee

    Root Mean Square Velocity of Gases

    This question came in NEET Exam 2018.Now my first query is that in the question,the mass of one Oxygen molecule is given wrong.Its exactly half it's true value.I don't think anybody has noticed this before because I couldn't find any change in the printed question on so many different books...
  14. Buzz Bloom

    I Formula: velocity of circular orbit wrt Schwartzschild metric

    Below are equations/formulas/text from https://en.wikipedia.org/wiki/Schwarzschild_geodesics https://hepweb.ucsd.edu/ph110b/110b_notes/node75.html I apologize for not remembering the source for the "v=" equation, or for my inability to find it again. For a circular orbit, the distance r and...
  15. LCSphysicist

    Motion under a force perpendicular to the velocity

    I think i could deal with this problem interpreting this force like a central force, what seems pretty nice to me, since in a circular orbit the force will always pass through the center, if it is perpendicular to the velocity. I thought, since the force is central and in this case, spherically...
  16. LCSphysicist

    Prisoner sliding down a rope with minimum velocity

    I thought in this equations f is the man's pull\ f + dm*g = T < 600 Where dm is equal to the mass of the string that pull the up part (15-x) after descending x meters. dm/(15-x) = m/15 And, to the man: W - f = Mx'' I can solve this, and i got ~8m/s Is this right?
  17. K

    Help with understanding this momentum problem

    Solution on the link: https://www.slader.com/textbook/9780321675460-university-physics-13th-edition/269/exercises/12/
  18. dkhurana

    I Four Velocity Vector: why divide by time according to the particle?

    So I understand that time is now part of the four vector, and so dividing delta X by delta t (time according to me), would produce just c as the first dimension of the vector, which gives us no intuition as to how fast time is moving for the observer, so is not useful. I understand why we...
  19. J

    Some Flight Calculations and the Motion of the Earth

    A Problem is posed for a flight from Melbourne to Cairns. Using the formula for rotational speed at latitude - 1) The latitude of Melbourne is approx 38 degrees south with a rotation velocity of 820 miles/hr 2) The latitude of Cairns is approx 17 degrees south with a rotation velocity of 994...
  20. hagopbul

    I Proper Velocity: Intro to Elementary Particles

    Hello : as i read during quarantine introduction to elementary particles by griffth i encounter the following paragraph "When we speak of the "velocity" of a particle (with respect to the labo- ratory), we mean, of course, the distance it travels (measured in the lab frame) divided by the...
  21. JD_PM

    I Understanding how to derive the relativistic-relative velocity formula

    I was studying how to derive the cross-section formula in the CoM frame from Mandl & Shaw QFT's book, and they state the following formula for the relative velocity (I'm going to use Vanhees71's notation though) $$\omega_1 \omega_2 v_{rel} = [(p_1 p_2)^2 - m_1^2 m_2^2]^{1/2} \ \ \ \ (2)$$ Then...
  22. I

    Exploring the Logical/Geometrical Explanation of Escape Velocity

    If you derive the equation for orbital velocity you get \begin{equation} v_{orbit} = \sqrt{\frac{GM}{R}} \end{equation} and for escape velocity you get \begin{equation} v_{escape} = \sqrt{\frac{2GM}{R}}=\sqrt{2}\,v_{orbit} \end{equation} I'm wondering if there is a logical/geometrical...
  23. jamiebean

    The final velocity = initial velocity + acceleration x time

    I first calculated initial velocity: √7.09^2+1.07^2=7.17028 acceleration=√7.22^2+2.47^2= 7.63 then i substituted all values into this equation: final velocity=initial velocity + acceleration x time so, final velocity=82.0285 so the magnitude= final velocity-initial velocity= 74.858271 is...
  24. jamiebean

    Velocity of bullet fired from a gun

    I first calculated the velocity v: √2.8^2+6.3^2= 6.8942 then i used it as the final velocity, so final velocity=6.8942 and the initial velocity=0 acceleration=9.8 Then i substituted them into this equation: final velocity=initial velocity + accelerationxtime then time=0.703489843 hence i...
  25. jamiebean

    Direction of resulting displacement

    I do not understand part b. I know that x180/pi changes the value into a degree, but i do not understand what's going on inside the bracket. And how did the equation calculated the direction?
  26. K

    What is the relationship between velocity and time on this graph?

    This is the graph I was given and the answer options. Since the graph is a straight line moving towards the positive direction I thought that meant it was traveling at a constant speed moving in the positive direction. That ended up being the wrong answer. Can anyone offer insight, I missed each...
  27. F

    Calculating velocity from the position versus time graph

    My answers: a) At points d the instantaneous velocity should be greatest since slope of c-d is greatest I think b) At point e and g instantaneous velocity is 0 c) at points b, c, and f instantaneous velocity is negative. Could you please verify my answers?
  28. A

    Power required to reach X velocity in X time with drag

    Hello, I wrote a program that adds force to a car like so: Engine Force = Power / Velocity Drag Force = -Velocity² Net Force = Engine Force - Drag Force = Power / Velocity - Velocity² I'd like to determine power based on how fast I want a car of a given mass to reach a given speed, for...
  29. G

    A rocket and its gas exhaust velocity

    This isn't right, is it? -\dfrac{GM}{R}+\dfrac12 v^2=-\dfrac{GM}{R+h} v=\sqrt{\dfrac{GM}{R}}\left( 1-\sqrt{\dfrac{R}{R+h}}\right) He's doing energy conservation. The mechanical energy at the Earth's surface is equal to the energy when the speed is 0.
  30. U

    Calculating Kinetic Energy Using Uniform Velocity and Energy Equations

    For: a) Avdol did the work because he is the force that is causing the displacement, right? b) Is there another formula we would have to use? I am confused at how this would work out and what the answer would be.
  31. Muhammad Danish

    Escape Velocity depends on the Radius of the Earth?

    We have 2 different formulas for escape velocity. and . If we look at the first formula we see that escape velocity is inversely proportional to the square root of Radius of Earth. While in the second formula, escape velocity is directly proportional to the square root of Radius of Earth. We...
  32. R

    Angular Velocity of a Car going around a curve

    θ=90°= π /2 so the instantaneous angular velocity dθ/dt= lim∆ t -> 0 (θ(t + ∆ t)-θ(t))/(∆ t) When I calculate it out it is π /2 radians per second. Is this correct?
  33. r-swald

    Find the escape velocity from 2 point charges

    Below is the work I've attempted. I used 2 PE b'c there were 2 point charges, and only one KE b'c only the proton is moving. The final equation in case it's hard to see is V(esc) = sqrt (4kQq / mr). I'm not sure if I did it right. Did I set up this equation right? and I am also not sure what...
  34. chucho11028

    Find the rate of change of velocity

    Hello everyone, I have a problem where I have to find the final displacement and final velocity which I have found however, I want to post few variations for that same problem which I am curious. It is more for my own knowledge > I would appreciate any help Please follow graph below with...
  35. Adec

    Comp Sci Galaxy simulation with the velocity Verlet algorithm

    To simulate the trayectories of solar systems around a black hole (i.e. a galaxy) I have 3 classes in C++: cSystem, cBlackHole and cGalaxy. cSystem assigns initial values of position, velocity, etc to a solar system. cBlackHole does the same but just for the black hole. And cGalaxy mixes...
  36. nomadreid

    I Lorentz boost -- speed or velocity?

    The Wikipedia article on Lorentz transformations is a bit confusing by its using speed and velocity almost interchangeably: of course γ (Gamma) stays the same, but (letting c=1) t'=γ(t-vx) , then if this is v⋅x, and x stays the same, then there would be a difference if something were going away...
  37. twilder

    I Scalar product of biharmonic friction with velocity components

    I know that taking the scalar product of the harmonic (Laplacian) friction term with ##\underline u## is $$\underline u \cdot [\nabla \cdot(A\nabla \underline u)] = \nabla \cdot (\underline u A \nabla \underline u) - A (\nabla \underline u )^2 $$ where ##\underline u = (u,v)## and ##A## is a...
  38. E

    I Velocity Vector Transformation from Cartesian to Spherical Coordinates

    Hi all, I can't find a single thing online that translates a cartesian velocity vector directly to spherical vector coordinate system. If I am given a cartesian point in space with a cartesian vector velocity and I want to convert it straight to spherical coordinates without the extra steps of...
  39. S

    Calculating Mean Velocity: Is Re Above 4000 Really Turbulent?

    First calculate mean velocity: 400 hl h-1 = 40,000 L / h-1 = 666.67 L/min 1L/min = 10^ -3 m3/min 666.67 L/min = 0.666 m3/min = 0.0111 m3/sec Cross sec area = (3.14)(0.1/2)^2 = 7.853 x 10^-3 m2 0.0111/7.853 x 10^-3 = 1.413 m/s Re = (1010)(1.413)(0.05)/0.0025 = 28,542.6 Am i right here? Re...
  40. Arman777

    I The magnitude of a four velocity

    I want to clarfiy some ideas, so let us assume an inital observer measures a 4 velocity of an object. ##\vec{u} = (c\gamma_u, \gamma_uu^x, \gamma_uu^y, \gamma_uu^z)##. When we calculate the magnitude of the 4-velocity we get, $$\vec{u} \cdot \vec{u} = -c^2\gamma_u^2 + \gamma_u^2U^2$$ where...
  41. M

    MHB Method of least square: initial position & velocity

    Hey! :o A point is moving linearly with constant velocity $v$ and the movement is $x=a+vt$. The below information is given: Find the initial position $a$ and the velocity using the method of least square. Could you give me a hint how we use this method here? Couldn't we use the data of...
  42. G

    To find the true velocity of wind from relative velocity

    Please can I ask for help with the following as to where I'm going wrong. Book answer is 20 knots and 315 degrees My solution: In the below diagram I have sketched the two situations, k is the true speed of the wind. First question is, is my diagram correct? The velocity of the wind...
  43. W

    B Measurement of an unknown velocity vector of a closed space

    Hi I found this paper on the measurement of unknown velocity vector of a closed space. Does it mean that it is possible to measure the unknown velocity vector of a closed space ? Can someone explain it to me
  44. V

    Finding the y-component of a velocity vector

    The first thing I did, was to find the equations for player A (p) and ball's (b) path (for each i and j component I used the equation I wrote in the relevant equations) and then I found the derivative of both equations so I could have the velocity: $$\vec{r}_p(t)=(6t^2+3t)\hat{i}+20\hat{j}...
  45. P

    Solving for earthquake transit time via Snell's Law

    I was told to solve the second equation above for x to get l2 and l2, but that only gets me those in terms of other unknowns. I'm assuming I just need to solve t for my knowns, but I keep getting caught up by my unknowns. i.e., solving for x gives x = (l2*L*v2)/(l1*v1+l2*v2). Please note "l" is...
  46. Ennio

    I Solar wind velocity and corrections

    Greetings, how do - the velocity distribution of the solar wind at 1 AU - the velocity distribution of the solar wind in our line of sight look like? I have found the 400 Km/sec but no further information. Is it an average values? Is this radially on the sun the same? Links with graphs are...
  47. J

    What is the kinetic energy when an object reaches escape velocity?

    What is the kinetic energy equal to during the escape velocity? Henceforth, what is exactly happening at the escape velocity in terms of gravity?
  48. patric44

    Derivation of the velocity of bloch electrons

    Hi guys I saw that equation of the velocity of electrons In a periodic potential $$ v = (1/h) grad E(k) $$ in my textbook we use in our solid state physics course without any proof or any thing and when I searched for it I found that its derived in Ashcroft book appendix E : Is there is any...
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