What is Velocity equation: Definition and 42 Discussions

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. Y

    B Terminal Velocity Equation in vertical cylinder with some fluid

    I just have a question that could you guys make an equation that expresses the terminal velocity based on followed condition? - When diameter increase, velocity decrease - velocity should change depending on both cylinder and sphere's diameter - We know every variable - The sphere is in...
  2. Krokodrile

    Velocity equation and distance problems

    I try to resolved with my knowlegde of the dynamic class: Acceleration is known to be the derivative of velocity with respect to time. a = dv / dt; so that dv = a dt Replace: dv = (2.4 - 0.6v inch/s^2) dt Then: dt = dv / (2.4 - 0.6v inch/s^2); we integrate t between 0 and 2; v between 0 and v t...
  3. 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...
  4. T

    Velocity equation for a cyclindrical tank and long pipe

    I was not really sure as to whether to ask this question here or the h/w forum as its something I am personally trying to understand. However, I shall let the admin decided. The question comes from a book called : . The specific question I have an issue with is not the question itself but the...
  5. J

    How Do Friction and Force Affect the Angular Velocity of Connected Wheels?

    Homework Statement A uniform cylindrical wheel of mass ##m_{1}## and radius ##R_{1}## rotates with angular velocity ##\omega_{1}##. It lies a certain distance (along the same axis) from a static wheel of radius ##R_{2}## and mass ##m_{2}##. The wheels are then pushed against each other with a...
  6. D

    Is the Faulty Velocity Equation for Projectile Launch Valid?

    I have seen this equation used to calculate the velocity of a projectile being launched off a table top. Where D=horizontal distance travelled, h=table height, and g=gravitational acceleration. Nowhere else can I find a calculation of velocity based on only two distances and GA. Everything I...
  7. S

    Terminal Velocity Equation with a Vi greater than 0

    Doing a skydiving project where the two people collide and move at an intital velocity of 75.73 m/s. When i use the normal terminal velocity equation i get: V = sqrt((2*m*g)/(DpA)) = 63.82 m/s When D is 1 p = .9798 A = .835 Is the a formula that factors in Vi? Or does it slow down to its...
  8. L

    Acceleration & max displacement from velocity equation

    Homework Statement The velocity of an object moving along the x-axis is given by Vx = (2.0t-t2)m/s. Initially (at t=0), the object was at the origin. a) Determine the object's acceleration at t=3.0s. b) Find the object's position at t=3.0s c) Calculate the object's maximum positive...
  9. Axidecimal

    V=? for Relativistic Mass,length contraction & time dilation

    Homework Statement Velocity Equations for Relativistic Mass,length contraction and time dilation. I was able to figure out one. This is not for homework. I want to learn these equations for future reference. Homework Equations The Attempt at a Solution Length Contraction : v = c...
  10. S

    B Integrating velocity equation problem

    I've already completed the first question, but with number two, it's a different case. Here's my attempt: \frac { d{ v }_{ y } }{ dt } \quad =\quad -g\quad -\quad \beta { v }_{ y }\\ \frac { d{ v }_{ y } }{ -g\quad -\quad \beta { v }_{ y } } \quad =\quad dt\\ \int { \frac { d{ v }_{ y } }{...
  11. Z

    Velocity Equation Derivation For Radiation Beaming

    Homework Statement [/B] Radiation beaming (cone) from an object traveling towards you at some velocity 'v' with the observed flux enhanced by an amplification factor 'a'. Derive an equation for the velocity 'v' needed to produce an amplification factor 'a'. Thank you Homework Equations...
  12. RJLiberator

    Understanding the Free Fall Velocity Equation

    Homework Statement I am tasked with coding some graphs regarding free fall motion. I am unclear what the professor means regarding the following, so I am looking for incite here. Problem: Solve numerically free fall velocity equation (problem 1.1), compare with exact solution (1.1) dv/dt =...
  13. B

    Linear velocity equation for a object trown vertically up

    Homework Statement The velocity of an object thrown vertically up in the air is given by V(t)=64-32t a) What is the average velocity during the first second? b) What is the average velocity between t=1 and t=3?The attempt at a solution a) displacement X1-X0 is given by the integral of v(t)dt...
  14. Dopplerganger

    Recognize this irreversible equation for kinetic modeling?

    Hi all, I'm trying to come up with velocity equations for a multi-enzymatic system and came across this velocity equation. Does anyone recognize this equation? There was no citation or derivation and the variables were not explained. This is my guess: P, Q, A, B are concentrations of some...
  15. T

    About velocity equation in simple harmonic motion

    Homework Statement Actually this is not a problem. This is about something i couldn't understand. Homework Equations where wt equals θ The Attempt at a Solution I can understand that x=r.cosθ it is obvious. But i can't understand why Vx=-V.sin(w.t) When i take a triangle from that...
  16. avito009

    What does the velocity equation prove?

    Does this equation v^2= \frac {2E_k} {m} prove that the velocity is inversely proportional to the mass of the object?
  17. K

    Derivative of an Angular Velocity Equation

    Homework Statement In reviewing my last physics exam I found the following statement in the posted solution: ...the derivative of \sqrt{\frac{3g}{l}(1-cos\theta)} is \frac{3g}{2l}sin\theta Homework Equations N/A The Attempt at a Solution This is from a physics course and I'm...
  18. S

    Position velocity equation free response

    Homework Statement A partcile starts att he point (1,0) and t=0 and moves along the x-axis so that at time t≥0 its velocity v(t) is given by v(t)= \frac{1+ t}{(1+t^2)} A) Determine the maximum velocity of the particle. B) Find an expression for the position s(t) of the particle at time t...
  19. H

    Velocity equation for quadratic drag, vertically thrown

    Homework Statement I am having some trouble deriving this velocity equation. I the net force will be [itеx] m * dv/dt = - mg - kv^2 [/itеx] Because the object is moving upwards. At the time t=0 the velocity will be [itеx]v(0)=v_0[/itеx] Homework Equations The Attempt at a Solution
  20. S

    Deriving position from a car's velocity equation.

    Homework Statement A driver sees the red light, and instead of braking the car, changes the gear to neutral. Suppose that velocity obeys this equation: v = v_0 * e^{-bt} Where v_o = 20 m/s and b = 0.150 s^{-1} a)Acceleration when time equals 0;(Answer:-3.0 m/s^2) b)Displacement when t=5.0...
  21. J

    Verifying Dimensionality of Fall Velocity Equation

    The equation for the fall velocity (terminal velocity) of a particle of a material in a viscous medium has been derived from theory as: Vt = gd^2(Pp - Pm) / 18 u Where: Vt is the terminal velocity in m/s; g is the acceleration due to gravity; d is particle diameter in m; Pp and Pm are the...
  22. P

    Showing the Terminal Velocity equation is dimensionally correct.

    Hey guys, this is my er...first post. It's a first year university physics assignment that I'm having a bit of trouble with, any help will be rewarded with kind words!(bit of an empty gift, but it's all I have) Ok, here's the problem. The terminal velocity of a mass m, moving at ‘high speeds’...
  23. M

    Calculating Friction Force from Velocity Equation

    Homework Statement A 12 kg box slides across the floor with an initial velocity of +8.4 m/s. It comes to a stop after sliding +13.8 m. How much friction was present? Homework Equations f=ma v^2=v(o)^2+2ad The Attempt at a Solution I did the ''v^2" equation to find out what the...
  24. C

    Integrating velocity equation to find position?

    Homework Statement For t < 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed vi. Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed: Fnet = −mkv2, where...
  25. G

    Solving time for a satellite to circle the earth using velocity equation

    Homework Statement The average speed of an orbiting space shuttle is 19800 mi/h. The shuttle is orbiting about 233 mi above the Earth’s surface. Assume the Earth’s radius is 3963 mi. How long does it take to circle the earth? Answer in units of h. Homework Equations I think it...
  26. L

    Proving the group velocity equation.

    Homework Statement A wave group is generated as a superposition of harmonic waves of average wavelength lambda. Show that V_{g}=V_{p}-\lambda \frac{d V_{p}}{d\lambda } The Attempt at a Solution All I know is that Vg = dw/dk and Vf = w/k. I am not sure what I need to do.
  27. H

    PLEASE HELP in Deriving Terminal Velocity Equation

    PLEASE HELP! in Deriving Terminal Velocity Equation :) Homework Statement The terminal velocity of a mass m, moving at 'high speeds' through a fluid of density ρ(kg m^-3), is given by v = sqrt(2mg/DρA) where A is the cross sectional area of the object (m^2) and D a dimensionless "drag...
  28. mccoy1

    Relative velocity equation help

    Hi folks, can someone please point out how Atkin got the following relative velocity A-B equation: see attached file. It's in atkin pchem 9e page 834. Thank you all.
  29. J

    Trying to derive a group velocity equation?

    hi, I am trying to derive the group velocity equation (actually its inverse): \frac{1}{v_g} = \frac{1}{c}(n(\lambda) - \lambda\frac{dn}{d\lambda}) where n is the refractive index and depends on the light's wavelength. I have started by saying that if v_g = \frac{\partial\omega}{\partial...
  30. M

    Deriving a Velocity Equation

    Homework Statement The Pitt Fall is thrill ride at Kennywood that lifts passengers to a certain height, pauses for a few moments, and then drops the riders, causing them to free fall towards the ground before gradually applying breaks 79 ft above the ground. Assume there is a drag force, F=-bv...
  31. T

    Calculating Velocity: Force, Mass & Distance Relationship

    I have a body of 1kg of mass being acted on by a force of magnitude equal (10000/(y^2)) [where y is the distance between the body and a certain point] and this force is in the direction pointing to the point so depending on what mentioned above :- what i know is : f = a = (1000 0/(y^2))...
  32. Z

    Just a quick question of the escape velocity equation

    Okay, I just found this new equation (new to me) for the escape velocity of a body. escape velocity = √(2GM)/R So say for instance I plug this into the escape velocity of the earth I am going to say the radius is 4001 miles so I it would take a mile above the Earth to escape (4001 * 1600) =...
  33. S

    Explanation to this velocity equation

    I have already done this problem enough times forwards and backwards to get the answer, so this is more of a theory question rather than help with homework. The equation for Vavg.=displacement/time or deltaX/deltaT. This equate to V=(X2-X1)/(T2-T1), correct? In working through a problem...
  34. J

    Trouble finding velocity equation

    Homework Statement The problem given has a(t) = C*t where C is a constant and equals 1.2 m/s^3 and t is time. It says velocity after 1.0 second is 5.0 m/s. The question is, what is the velocity after 3.6 seconds. I don't know if I can integrate to get the velocity equation or not. Please...
  35. C

    Dynamics: Projectile Motion velocity equation

    1. "A projectile is fired with a velocity u at the entrance A of a horizontal tunnel of length L and height H. Determine the minimum value of u and the corresponding angle \theta for which the projectile will reach B at the other end of the tunnel without touching the top of the tunnel."...
  36. K

    Calculate Minimum Speed for Ball to Clear Roof - Velocity Equation Help

    You're 6.0 m from one wall of a house. You want to toss a ball to your friend who is 6.0 m from the opposite wall. The throw and catch each occur 1.0 m above the ground. V Assume the overhang of the roof is negligible, so that you may assume the edge of the roof is 6.0 m from you and 6.0 m from...
  37. M

    Calculating Average Velocity for a Bike Ride

    Homework Statement You ride your bike for 1.5h @ avg velocity of 10km/h, then for 30min @ 15km/h What is you average velocity? So I think that the variables are this Vf=15km/h(.000004m/s) Vi=10km/h(.000003m/s) Tf=90m(5400s) Tf=30m(1800s) Homework Equations That's what I'm asking -_- I...
  38. D

    How Can You Solve the Differential Equation a=dv/dt=-Cv^2 for v(t) and x(t)?

    Given a(t) = -Cv^2(t) where C is a constant, express v(t) and x(t) as explicit functions of time t. Assume v(0) = v0 So I tried integrating both sides of the equation to get: v(t)+C' = -C integral v^2(t) dt but then I how am I supposed to integrate v^2(t) dt... Also, I thought I could do it...
  39. H

    What is the average velocity equation?

    1. When I see the variable v at some place, how do I know as to whether v is being defined as velocity or speed? On Wikipedia both, velocity and speed, are referring to a formula with v. 2. What is the average velocity of the following: http://img226.imageshack.us/img226/3798/veloc0zt.jpg...
  40. D

    Is there a simpler explanation for the equation \omega=\frac{2\pi}{T}=2\pi f?

    I saw this on Wikipedia \omega=\frac{2\pi}{T}=2\pi f = v/r What I don't understand is \omega= \\ \frac{2\pi}{T}=2\pi f How can they be equivilant? Thanks
  41. J

    What is the equation for calculating terminal velocity?

    i'm looking for an equation to calculate terminal velocity. Does anyone know it? and can u please post in here please. :smile: