What is Velocity vector: Definition and 99 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. M

    I need to find the velocity vector two results help please

    Homework Statement find the velocity vector for the time t=2s i have given r(t)= (50*sin((1/2)*t)*cos ((1/4)t), -50*sin((1/2)*t)*sin((1/4)t)) Homework Equations i also know that r(t)= (50*sin(k*t)*cos (1/2k*t), -50*sin(k*t)*sin(1/2k*t)) where k = 0,5s-1 The Attempt at a...
  2. J

    Determining wind velocity vector.

    Homework Statement A light plane is headed due south with a speed of 185km/h "relative to still air". After 1.0hr, the pilot notices that they have only covered 136km. And that their direction is Southeast 45 degrees. What is the wind velocity? Homework Equations Im guessing you have to...
  3. S

    Position and velocity vector of point referred to equinox

    I'm looking at a book on meteor calculations involving at two Earth stations, A and B. The computations for A are given, and the same for B. I would like to know a reference for equations 12, 13, and 14. Even a derivation. I find figure 4 a bit puzzling. The text uses lower case phi, a...
  4. W

    Velocity Vector has Coordinate-Independent Meaning

    Hi, All: It's been a long time since I did this, and I have some basic doubts; please bear with me: In Lee's Riemannian Mflds, p.48, he states that , given a parametrization : γ:(a,b)→M, of a curve , "the velocity vector γ'(t) has a coordinate-independent meaning for each t in M"...
  5. F

    Magnitude of a velocity vector with special relativity

    Hi, I'm trying to get my head around how velocity vectors work in special relativity. For example, in classical mechanics, the magnitude of the velocity would be given by: v^2 = \sqrt{v_x^2 + v_y^2 + v_z^2} where v_x, v_y and v_z are the x, y and z components of the velocity...
  6. S

    Find v(t) the velocity vector of a projectile given a(t).

    Homework Statement Suppose we have a projectile launched from an initial height of h ft with initial speed V0 ft/sec and angle of elevation theta. We will attempt to model air resistance by assuming acceleration vector given by... a(t)=...
  7. M

    What is the angle of the velocity vector of a released package?

    Homework Statement An airplane with a speed of 96.8 m/s is climbing upward at an angle of 74.0 ° with respect to the horizontal. When the plane's altitude is 906 m, the pilot releases a package. (a) Calculate the distance along the ground, measured from a point directly beneath the point of...
  8. M

    Radial component of a velocity vector - cylindrical coordinates

    Hi there, I'm trying to determine the radial component of a velocity vector in a disk. The vector doesn't (necessarily) start from the centre of the disk and can be pointed in any direction. I've attached a .pdf with the schematics - it seems like a simple problem but it has me stumped...
  9. A

    Kinetic Energy from Velocity Vector

    I just need to find the kinetic energy of a 3.00kg object moving with a velocity <6,-1> m/s. I should be able to take the dot product to find v-squared right? I find that v^2=37, multiply by 3, divide by 2, this gives 55.5 J, the book says 60.0 J. I can't figure out what the problem is.
  10. L

    Show magnitude of velocity vector in polar coordinates

    Homework Statement In Cartesian coordinates the magnitude of the velocity vector squared is |v|^2=V*V= Vx^2 +Vy^2 =(dx/dt)^2+(dy/dt)^2 Show that in polar coordinated |v|^2= Vr^2 +V@ ^2 Homework Equations The Attempt at a Solution Not really sure what the question is asking me to...
  11. ThomasMagnus

    Average Velocity Vector Diagram

    Homework Statement Homework Equations The Attempt at a Solution I thought it was "D". The correct answer is "A". Can you help me figure out why?
  12. R

    Relative Velocity Vector question

    Homework Statement An airplane is heading due south at a speed of 600km/h. If the wind begins to blow from the southwest at a speed of 100km/h (average), calculate: a) The velocity (magnitude and direction) of the plane relative to the ground b) How far from its intended position will it be...
  13. S

    Car-Minivan Collision: Final Velocity Vector

    Homework Statement A car with a mass of 1000 kg traveling with a velocity of 15m/s east collides with a 1200 kg minivan traveling at a velocity of 20m/s north. After the collision the car and the minivan are stuck together. Draw to the scale the final velocity vector of the car and minivan...
  14. S

    Deriving angular velocity vector algebra?

    where x represents cross product currently if i forget i figure these out using the right hand rule, but how do you get each equation visa versa using vector algebra i started with w = rxv how do you derive that v = wxr i got up to this w = rxv w= -(vxr) rxw = -rx(vxr) rxw =...
  15. J

    Finding the limit of a velocity vector

    Homework Statement A particle moves in the XY plane so that at any time t is greater than or equal to 0 its position (x,y) is given by x = e^t + e^-t and y = e^t - e^-t. Find the limit as t approaches infinity of dy/dx. Homework Equations I found dy over dx to be e^t + e^-t over e^t...
  16. T

    Obit velocity vector variances, how it works?

    Why does the moon have a decelerated velocity on one half of its orbit and on the other side it has an accelerated velocity. And why is this same with the earth. From my data the variances in velocities of Earth affect the velocity variance of the moon. So I have been able to create a formula...
  17. T

    Confused about uniform circular motion (and it's velocity vector)

    Sorry if this is the wrong (sub)forum! I need some help to understand how to express the following: The velocity vector When this is given: Omega radius Both in magnitudes. I want to obtain an expression for the velocity vector when the angle theta (radians/s) is changed. That...
  18. D

    Height of Ball with Velocity Vector

    Homework Statement A ball is projected horizontally from the edge of a table that is 1.02 m high, and it strikes the floor at a point 1.28 m from the base of the table. What is the initial speed of the ball? Correct, computer gets: 2.81e+00 m/s How high is the ball above the floor...
  19. S

    Derivative of velocity vector?

    Hi, I'm trying to get a geometric idea of what the derivative of a velocity vector is. For example if you're talking about the space between vx and vx + dvx, where vx is a velocity along the x axis. Would it be like an infinitesimal sphere around the end of the vector? Thanks... (Added...
  20. V

    Calculating the Velocity Vector of a Tennis Ball

    Trying to get my head around the velocity vector that a tennis ball goes after it is hit with a tennis racket. To make matter easier, I am only thinking about it in terms as if the ball is sitting in midair motionless when the racket hits it. Say the ball is hit with a force of 1N and the...
  21. M

    Velocity vector along a parabola

    Hello, I'm new here and wasn't sure if this should be put into the homework section. It's not a homework question but the nature of the problem is homework-ish in nature I suppose. Anyway I'm trying to understand why a velocity vector along a parabola would have the same initial velocity as...
  22. D

    What is the equation for finding the velocity vector of a component?

    Homework Statement http://img705.imageshack.us/img705/20/33060912.png Homework Equations http://img706.imageshack.us/img706/7514/67377660.png The Attempt at a Solution I don't understand how they find equation number (5). Can somebody help me with this?
  23. I

    Angular Momentum, Torque, and Acceleration for a Moving Body

    The velocity of a .5kg body, for t=1s to t=35s, is given by v=5t^2 i + 3/t j -t k v has - over it...and the i, j, and k have the hats on them (^) For this interval, What is the body's angular momentum? What is the torque exerted on the body? what is the acceleration of the body? what...
  24. A

    Accelerometer data to a useful velocity vector

    Hello Everybody, Currently I am working on my diploma thesis, which is to provide an auxiliary vector for a WLAN based RTLS (Real-time locating system). Because it has flaws in it, that come from losing IP packets, I have to construct an auxiliary system to it based on vectors. I am...
  25. P

    Calculating Velocity Vector Below Niagara Falls Edge

    Suppose the water at the top of Niagara Falls has horizontal speed of 3.59m/s just before it cascades over the edge of the falls. At what vertical distance below the edge does the velocity vector of the water point downward at a 64.1 degree angel below the horizontal? From this information I...
  26. C

    Components of Earth's angular velocity vector

    Homework Statement Using a coordinate system in whic x and y are due east and nort of the city and z is the radial distance outwards from te centre of te earth, find the compnents of w the Earth's angular velocity vector. You may assume that the latitude of the city is lamdba = 34degrees...
  27. E

    Paramaterization of position and velocity vector

    Homework Statement A stone is thrown from a rooftop at time t = 0 seconds. Its position at time t is given by r(t) = 10ti - 5tj - (6.4 - 4.9t^2)k: The origin is at the base of the building, which is standing on at ground. Distance is measured in meters. The vector i points east, and k points...
  28. P

    Velocity vector and Max Height

    This is a question from "Fundamentals of Physics 8th Edition Extended, Chapter 4, Checkpoint3." "At a certain instant, a fly ball has velocity v->=25i-4.9j (the x-axis is horizontal, the y-axis is upward, and the v-> is in metres per second). Has the ball passed its highest point? The...
  29. T

    Position and Velocity Vector

    A point M is located by the vector r(t), which depends on time, but the length of r(t) is constant. Show that the velocity v(t) of M is perpendicular to r(t).
  30. I

    Find the magnitude of the velocity vector on impact

    (resolved) find the magnitude of the velocity vector on impact Thelma and Louise drive their '66 T-Bird convertible off a cliff. They are going 25.9 m/s and the cliff is 97 meters high. Find the magnitude of their velocity vector the moment they impact the ground. Make sure you do the following...
  31. I

    Center mass/angular velocity vector

    Homework Statement baton like figure - weight at (0,A) that has a mass M, second weight at origin (0,0) with weight 2M. These are the end points of the baton and that is it for this baton weight/location. The 2M weight has a velocity V towards the positive x axis. The goal is to locate the M...
  32. H

    Simple velocity vector problem; IS MY SOLUTION MANUAL WRONG OR AM I?

    Simple velocity vector problem; IS MY SOLUTION MANUAL WRONG OR AM I?! Homework Statement A particle starts from the origin with velocity 5i at t=0, and moves in the xy plane with a varying acceleration given by a= 6 Sqrt(t) j, where t is in s. a.) Determine the vector velocity of the...
  33. C

    Position vector and velocity vector

    Hi everyone, Could someone please help me on this problem? Homework Statement A particle initially located at the origin has an acceleration of a=1.00jm/s^2 and an initial velocity of V=8.00im/s a. Find the position vector at any time t (where t is measured in seconds) b. Find the...
  34. L

    Velocity Vector Versus Tangent Line

    I have encountered a problem in my Calculus homework. I have a position function, r(t)= (t^2)i + (4t)j and in my homework, I am asked to find the tangent to this curve at the point t=3. I did this by finding dy/dx, or 2t/4 @ t=3 is 6/4. However, I am also asked to relate this to the...
  35. B

    When will the velocity vector make an angle of 45 degrees?

    i have been given that vector r = bt^2i + ct^3j where b and c are positive constants, and i need to know when the velocity vector will make an angle of 45 degrees. i have been trying to figure it out and am just confused. i have taken the derivative of vec r, because i know that it becomes...
  36. M

    Vertical Component of a Velocity Vector

    Homework Statement http://img256.imageshack.us/img256/5530/hwimgxd3.gif A particle of mass 0.450 kg is shot from P. The particle has an initial velocity V_0 with a horizontal component of 30.0 m/s. The particle rises to a maximum height of h = 21.0 m above P. Assume that h2 = 62.0 m...
  37. Saladsamurai

    Average velocity vector question. Try again

    Homework Statement A train with constant velocity of 60km/hour travels east for 40minutes; then in a direction 50degrees east of north for 20minutes; then west for 50minutes. A)What are the magnitude and B) angle of its average velocity during the trip? Homework Equations sinx; cosx; tanx<--...
  38. B

    Solving for Velocity Vector Angle of 45.0

    Homework Statement If http://net.dinhweb.de/vector.gif ,[/URL] where b and c are positive constants, when does the velocity vector make an angle of 45.0 with the x- and y-axes? Homework Equations I'm not sure.. I've got a million equations but none of them seem to fit the problem the way I...
  39. L

    What is the angular velocity vector of a rotating rod?

    The problem has a picture of a rod on a 3 dimensional coordinate system and gives the measurements. The rod rotates around the line joining each of the two endpoints with a constant angular velocity of 12 rad/s. The problem has you do things in steps, first finding the components in x, y...
  40. S

    Calculating Velocity Vector after Ball Impact with a Surface

    Hi, I'm trying to figure out how to calculate the resulting velocity vector of a ball after impact with a surface. If the velocity vector is V {Vx, Vy, Vz} and The ball hits a surface with normal N {Nx, Ny, Nz} what would be the resulting vector of the new velocity? Assuming the ball...
  41. S

    Projectile Motion (Displacement and Velocity vector)

    hey guys, i have this question I am diong, i got allt he answers but there's one prob Question: A projectile is fired at 50 m/s and 60 degrees along a level surface. a) Find the velocity and displacement VECTORS at t = 1.0 s i used v2 = v1 + at v2 = 43.3 + (-9.8) (1) v2 = 33.5 m/s...
  42. B

    Uniform circular motion and velocity vector

    hi Object in uniform circular motion is moving around the perimeter of the circle with a constant speed and while the speed of the object is constant, its velocity is changing . The direction is always directed tangent to the circle To my question . Velocity vector at particular point A...
  43. G

    What's the velocity vector to hit a ground target.

    I'm a computer programmer, but I'm having trouble with this one. I need help figuring out how to calculate a 3D velocity vector which will make a projectile follow an ARC between two points on the ground, firing with a fixed speed. I have a cannon at point a (x, y, z) I have a target on...
  44. A

    Solving Exercise: Finding Velocity Vector of Cyclist

    Hi! I have an exercise here that I can't solve. Help please. "One of two cylists cycles in the north-west direction at a speed of 8 m/s making an angle of 53 with the west. The other cyclist cycles in north-east direction at a speed of 6m/s making an angle of 37 with the east. How does the...
  45. T

    Find the velocity vector for the particle at any time

    During the time period t=0 to t=6 seconds, a particle moves along the path given by x(t)=3cos(pi*t) and y(t)=5sin(pi*t) 1. Find the velocity vector for the particle at any time t. 2. Write and evaluate an integral expression, in terms of sine and cosine, that gives distance the particle...
  46. W

    Help with velocity vector and friction questions

    I can't quite get an answer for these damn questions. It feels like there is information missing. 1. Show that the minimum stopping distance for a car traveling at speed v is equal to v^2 / 2*coefficient of friction*g, where the coefficient of static friction is between tires and the road...
  47. S

    Regarding the direction of the angular velocity vector

    If a top is spinning in the horizontal x,y planes in a counter-clockwise motion, the vector of its angular velocity and acceleration is perpendicular to that plane, specifically in the positive z direction. Is there any specific reason for direction? My book states that the vector must be...
  48. S

    How to Draw Velocity Vectors for a Car on a Racetrack?

    Here we are looking down on a racetrack with straight sections and semicircular ends. A car is going around the track and maintaining constant speed. For each one of the numbered positions: Draw diagrams showing the velocity vector for the car. I will post my diagrams on a separate reply...
  49. T

    Calculate the velocity vector as a function of time

    Hi, Ok I have a bit of difficulty workin this Physics Mechanics problem. Ok here is the problem... The coordinates of a plane flying in the xy-plane are given as functions of time by: X = 2.0m - at Y = bt^2 where a = 3.0 m/s and b = 2.5 m/s^2 A) Calculate the velocity vector...
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