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. L

    Elliptical motion in polar coordinates

    I think I have completed the exercise but since I have seldom used polar coordinates I would be grateful if someone would check out my work and tell me if I have done everything correctly. Thanks. My solution follows. Since ##\left(\frac{x}{a}\right)^2+\left(\frac{y}{b}\right)^2=1## it follows...
  2. L

    Solving a Celestial Mechanics Task with Velocity Vector Scattering

    Hi, the task is as follows Unfortunately, I am not getting anywhere at all with task c. I have now proceeded as follows: I assume that the calculation takes place in the reference system of the sun. In the task the following is valid, $$\vec{v}_{si}=-s\vec{v}_p$$ I have now simply assumed...
  3. hjam24

    Determine vertical velocity vector on sloped surface

    A golf is launched at a speed v,f and launch angle, β,f. The slope of the green is equal to φ. At some point the ball is located on the rim of a hole. The side view (a) and overhead view (b) looks as in the attached image.According to the author of the [paper][2] "The Physics of Putting" the...
  4. Gamma Anon

    I Is the Killer Crate Paradox Resolved?

    Hi Physics Forums, I've devised a thought experiment called the "Killer Crate Paradox" to put a spotlight on an issue I'm having, with regards to understanding length contraction, specifically in instances where multiple objects are observable and they have different velocities and directions...
  5. V

    Direction of of the velocity vector for particles in a sound wave

    Using the equations mentioned under this question, I came up with following analysis and directions of velocities on either side of ##x_1##. Also, I'm not sure if there is an easier qualitative way to know the velocity directions rather than do a detailed Calculus based analysis?
  6. E

    Velocity vector addition problem

    Hello, guys. Interesting riddle here. I have no idea how to solve it. Tried different methods, but point is answer is always wrong, exact answer Downriver, at an angle of 53.13(degree) to the bank. That exercise is from "Pohl’s Introduction to Physics"
  7. WMDhamnekar

    MHB What is the velocity vector after a pinball bounces off a baffle?

    Hi, A pinball moving in a plane with velocity s bounces (in a purely elastic impact) from a baffle whose endpoints are p and q. What is the velocity vector after the bounce? I don't understand how to answer this question? Any math help, hint or even correct answer will be accepted?
  8. winnie_d_poop

    Prove that the derivative of the position vector equals the velocity vector

    1.)##\dot{\vec{r}}=\dot{x}\hat{i}+\dot{y}\hat{j}+\dot{z}\hat{k}=\dot{r}\hat{r}## since the unit vector is constant 2.) ##\dot{r}\hat{r}=\frac{x\hat{i}+y\hat{j}+z\hat{k}}{\sqrt{x^2+y^2+z^2}}\frac{\dot{x}x+\dot{y}y+\dot{z}z}{\sqrt{x^2+y^2+z^2}}##...
  9. justinpaul

    Calculating Velocity Vector of Object in 2D Space

    The question I am trying to solve is what is the velocity vector (direction and magnitude) of an object in 2 d space. We know the distance measured to the car from two different angles. We know the radial velocity of the car on both measurements. The radial velocity is the component of the...
  10. E

    Finding time from a velocity vector

    I've looked it up online and someone did t=40−65=0.15(h) I was just wondering why they would subtract the velocities. Could something explain this to me please? thanks.
  11. 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.
  12. 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...
  13. 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...
  14. 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
  15. 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}...
  16. Adesh

    A question of kinematics involving a changing velocity vector

    The statement "at the initial moment of time v ⊥ u and the points are separated by a distance l " gives us a picture like the one which I have added in attachment. As the time passes velocity vector v would gradually change from fully vertical to fully horizontal in order to meet point B. Now...
  17. R

    I Unknown velocity vector of a rail carraige

    referring to the image in fig 1 there is a rail carriage subject to an unknown velocity vector Vu (velocity unknown). Vu has a constant velocity Vu in the direction as shown. In the ceiling of the carriage is a light shown in blue and a columnator on the floor. The rail carriage is sitting on...
  18. ashhlyn

    Finding the expression for the x-component of velocity (vectors?)

    Homework Statement a particle's position is the vector r=(ct^2-2dt^3)i+(4ct^2-dt^3)j where c and d are positive constants. find the expression for the x-component of the velocity (for time t>0) when the particle is moving in the x-direction. you should express your answer in terms of variables...
  19. G

    Angular Velocity Vector; Relationship to Angular Momentum

    I read in several places that if, for example, a point particle exhibits uniform circular motion about the z-axis within an osculating plane not equal to the x,y plane, then the angular velocity still points along the z-axis, even though the angular momentum does not (it precesses about the...
  20. T

    Calculate the Curl of a Velocity vector field

    Homework Statement The velocity of a solid object rotating about an axis is a field \bar{v} (x,y,z) Show that \bar{\bigtriangledown }\times \bar{v} = 2\,\bar{\omega }, where \bar{\omega } is the angular velocity. Homework Equations 3. The Attempt at a Solution [/B] I tried to use the...
  21. Poetria

    Circular motion - velocity vector

    Homework Statement Which of the following correctly describes the velocity vector in each case? 2. The attempt at a solution I got it wrong at first. My new attempt (I have a sneaking suspicion that I am missing something important): For the first picture: dtheta_1/dt<0 - the angle is...
  22. L

    Projectile Motion velocity vector Problem

    I want to know if i did this problem correctly! Problem: A projectile is traveling with velocity vector v = (30.00 m/s)i + (20.0 m/s)j when it experiences an acceleration of vector a = (-10.00 m/s^2)j. What is its velocity after 2.0 s? What is its speed after 2.0 s? My work: Vy = V0y - gt =...
  23. S

    Find angle between displacement and velocity vector

    Homework Statement A stone is thrown at 25m/s and at 37 degrees above the horizontal from a 20m high building. Take g=10m/s2 Let D be the displacement vector from launch point on top of the building to landing point on the ground, and v be the velocity vector on impact, what is the angle...
  24. Pushoam

    Difference: mean velocity & modulus of mean velocity vector

    Homework Statement Homework EquationsThe Attempt at a Solution [/B] A) Mean velocity is defined as <v> = total distance traveled/ total time taken = πR/Γ = 0.5 m/s B) How is part a) different from part b)? I think what Irodov means by mean velocity is mean speed in part a. It is mean...
  25. S

    Finding the magnitude of velocity vector

    Homework Statement A cricketer throws a 147g ball by exerting a force of 7.5N for 0.84s. If the launch angle is 39 degrees from horizontal, calculate the range of the ball. Homework EquationsThe Attempt at a Solution I have the range equation and I just need to find the magnitude of the...
  26. R

    I Can a Velocity Vector be Integrated to Parameterize y=x^2?

    Hi (1/sqrt(4t²+1), 2t/sqrt(4t²+1)) gives a unit tangent to the curve y=x^2 at point (t,t^2). Viewing the vector as velocity, shouldn't I be able to integrate it and get a parameterization for y=x^2?
  27. Arman777

    Where the Angular Velocity Vector Coming From?

    I know that If we have a rigid body rotating clokwise direction,the angular velocity vector should be in the into the screen.But also I know that ##w=dθ/dt## so..Whats the equation that tells us that ##\vec w## is into the screen ? Is it coming from some vector product ? Or we know that...
  28. doktorwho

    Velocity vector and velocity intensity

    Homework Statement Given the velocity vector in the polar coordinates, ##\vec v=-awsin{wt}\vec e_r + awcos{wt}\vec e_\theta## determine the average velocity vector and velocity intensity over a time period ##[0, \pi/2w]## Homework Equations 3. The Attempt at a Solution [/B] For the first part...
  29. C

    Average velocity vector of non-uniform circular motion?

    Homework Statement A particle starting from rest revolves with uniformly increasing speed in a clockwise circle in an xy plane. The center of the circle is at the origin of an xy coordinate system. At t=0, the particle is at x=0.0m, y=2.0m. At t=2.0s, it has made one-quarter of a revolution and...
  30. M

    Calculating Velocity Vector for Cue Ball Collision

    Homework Statement I need to find the velocity vector of the cue ball. I know the start-coordinates, end-coordinates(when it hits the red ball), and the time it takes for the travel, but i have no clue on how to make the vector. start(21, 0) end(21, 12) time = 0.1seconds not sure if...
  31. D

    I Velocity Vector Fields: Differentiating a Vector Function to Scalar

    Hi. Given a one-parameter family of maps such as Φt : ( x , y ) → ( xet + 2et -2 , ye2t ) the velocity vector field at t=0 is given by d(Φt)/dt = (x+2) ∂/∂x + 2y ∂/∂y My question is ; how does differentiating a vector function Φt with respect to t result in a scalar function ? Thanks
  32. H

    Relation between position vector and velocity vector

    The equation following (3.80) seems to suggest that the velocity vector ##\vec{\dot{r}}## must always be parallel to the position vector ##\vec{r}##. But clearly this is not true as a particle's velocity can be in any direction. What's wrong?
  33. J

    What are the x- and y-components of the velocity vector?

    Homework Statement Question is: What are the x- and y-components of the velocity vector shown in the figure? https://session.masteringphysics.com/problemAsset/1384003/6/knight_Figure_03_22.jpg The Attempt at a Solution I tried -100 m/s*cos(30 degrees)=-86.6m/s for the x component and...
  34. NiendorfPhysics

    Velocity Vector at the end of the acceleration formula?

    Homework Statement Don't ruin the problem for me please, I just want to know why there is a velocity vector at the end of this formula. It's really strange since there is velocity in the equation already, so what would the velocity with the vector arrow on top mean? Problem: A boat travels at...
  35. V

    Velocity and acceleration vectors

    Question #7. It says: The (constant) acceleration points in the direction of the difference of the velocities (final minus initial). Note how initial vector is subtracted from the final one (head to tail). But in this video, average acceleration (change in velocity) is found by adding velocity...
  36. Poetria

    How Is Average Velocity Calculated in Circular Motion?

    Homework Statement A bicyclist makes a three quarter turn of radius 1.5 m at constant speed. During the turn, the only horizontal force acting on the bicyclist is a static friction force of constant magnitude 250 N. The total mass of the bicycle and rider is 60 kg.Homework EquationsThe Attempt...
  37. Toon

    Velocity vector displacement problem

    1.)Hey everyone! I am having some trouble with a problem and hoped someone might be able to steer me in the right direction! The problem states , A motorist drives south at 20.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.00 min, and finally travels northwest at 30.0 m/s for...
  38. D

    Velocity graph, a ball is thrown upward

    I don't get it, why is the graph always linear? Shouldn't its slope be zero when the ball is at the top and stops there for a moment? The way it is "explained" is that it's at the top for instantaneous moment. Okay, but, if let's say, ball was going upward for a 5 sec, then stopped for 1 second...
  39. P

    Proving Velocity Vector Magnitude Equals c

    Homework Statement show that ## V\prime=\sqrt{ V_{x}^\prime{ ^2} + V_{y}^\prime{ ^2} + V_{z}^\prime{ ^2}} = c## -------------1Homework Equations ##V_{x}^\prime{ ^2}=\frac{V_x - V }{1-{\frac{V V_x}{c^2}}}## -----------------2 ##V_{y}^\prime{ ^2}=\frac{V_y...
  40. C

    Finding the angle of the velocity vector of a projectile at moment of impact

    Homework Statement A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 16.0 m/s. The cliff is h= 41.0 m above a flat horizontal beach h=41 g=10m/s vi=0m/s vf2=vi2+2gh vi=28.64 h=vi+vf/2xt 41=28.64/2xt 14.32 t=2.86 28.64x28.64, 16x16 Square...
  41. T

    Direction and velocity vector problem

    Homework Statement At one instant a bicyclist is 60 m due east of a park’s flagpole, going south at 20 m/s. Then 30 s later, the cyclist is 40 m due north of the flagpole, going due east with a speed of 10 m/s. On an XY-coordinate system with the flagpole at the origin, for the cyclist in this...
  42. A

    Free-body diagram velocity vector

    My teacher gave me a solved problem to practice. There is a free-body diagram of a particle on a tilted plane. The resulting force points in the direction of the negative x-axis, aligned with the inclination of the plane.Am I the only one that thinks there could also be a velocity vector...
  43. M

    Find F2 on a particle given velocity vector and F1 vector

    Homework Statement While two forces act on it, a particle is to move continuously with v = (3 m/s)i - (4 m/s)j. One of the forces is F1 = (2N)i + (-6N)j. What is the other force? Homework Equations My main problem is with the verbiage, "move continuously". Does this suggest constant...
  44. U

    Find the velocity vector of a curve at point r(t)

    Homework Statement What is the velocity vertor of a particle traveling to the right along the hyperbola y=x-1 which constant 5 cm/s when the particles location is (2, ##\frac{1}{2}##)? Homework Equations The Length of path forumula. $$ s\,=\int_a^b ||r'(t)||\,dt $$ Please don't make me...
  45. B

    What is the Effect of Motion on the Velocity Vector of Light?

    Hi, Consider a source of light transmitting light at an angle θ with x-axis as seen in the following figure: Now an observer looking at x-axis will determine the speed of light to be c.cos θ, and the one looking at y-axis determine c.sin θ. How can we resolve this according to the...
  46. V

    Velocity Vector in Polar Coordinates (Kleppner p.30)

    In polar coordinates we have \vec{r} = r \hat{r} \Rightarrow \vec{v} = \frac{d}{dt}({r \hat{r}}) = \dot{r}\hat{r} + r \frac{d \hat{r}}{dt} . In the book Introduction to Mechanics, K & K says the right term is the component of velocity directed radially outward. (Surely a typo, as the left...
  47. R

    How do you connect angular velocity vector with the positions?

    I've been working out a question about rigid body rotations, and though I can grasp the basic math, I'm completely lost about the physical quantities. In particular, I'm trying to relate the three components of the angular velocity vector that I found with the physical picture: Suppose that...
  48. G

    Speed and direction of Velocity Vector - Inelastic

    Homework Statement A 55kg man is running in the positive y direction at 4 m/s. He is tackled by a 115kg man running 8.5 m/s at a 140 degree angle. What is the speed and direction after the inelastic collision? Homework Equations p=mv p = sqrt of x^2 + y^2 The Attempt at a Solution...
  49. A

    Change of the angular velocity vector

    Homework Statement I don't know how to solve part(b). See the photo Q3 for the question. Homework Equations The Attempt at a Solution See the photo 2010Q3 I found the torque and hence the new angular momentum vector. But I wonder how could this help me to find the angle...