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. A

    A massless disk with an embedded particle rolls down an inclined plane

    This is the problem: I am a little confused at the solution below. Since ##\vec r_{P/C} = (R/2)*(5 + 4cos(\theta))^{0.5}\ \vec e_r##, I am wondering why there is no vector e_r component for the velocity. I know that d(R)/dt = 0, but you can still get a derivative in the ##\vec e_r## direction...
  2. User849483

    Need help finding uncertainty for this equation

    this is the formula v is velocity g= gravity h= height ro= outer radius of cylinder ri = inner radius of cylinder please help
  3. chwala

    Find the velocity of the stone just before it hits the ground

    In my lines i have, ##h(t)=ut+\dfrac{1}{2}at^2## where ##u=0##, with ##a=10##, ##h = \dfrac{1}{2}×10t^2## ....................1 ...also, ##h-14.7 = \dfrac{1}{2}×10 (1.4-t)^2## ..................2 1- 2 gives, ##14.7 = 14t -9.8## ##24.5=14t## ##t=1.75## Therefore, ##v = 10×...
  4. E

    How Can Derivatives Determine Speed in Physics Problems?

    I have been trying to solve this problem for hours using the mentioned equations but no matter what I do I cannot get the correct answer, that is v = 22.4 m/s. I thought that maybe if I could get an expression where v is a function of time I could solve the problem but I don't know how to do...
  5. clueless_roboticist

    I Work done along a path: how does velocity play into it?

    To boil down the question, if you have a body at rest and apply a constant force, it will accelerate and the work done on it will be F*s (or the integral version of that statement). However, as the body accelerates due to the force, does that mean, per a given time unit, more and more work will...
  6. brotherbobby

    Distance-time graph of a ball throw vertically up from a fixed point

    Statement of the problem : I copy and paste the statement of the problem to the right as it appeared on the website. Given below is the graph of the ball as its distance from a fixed point with time. Attempt : Where does this fixed point, say ##\text{P}## lie? Imagine the fixed point lied...
  7. A

    Constrained motion of a ring along a horizontal rod

    The correct answer is u=vcos\theta. I have understood so far to be able to conclude that \text{displacement of string} = PA - PC \approx AB Also, \overline{AB}=\overline{AC}cos\theta or, more generally, \vec{S}_{along\ the\ string}=(\vec{S}_{along\ the\ horizontal})cos\theta Now, I had hoped...
  8. indefiniteintegral

    Solving for φ on an oscillation problem

    position and velocity expressions for the initial conditions 1) x(0)=Acosφ = xi 2) v(0)=-ωAsinφ= vi Dividing 2nd equation by equation results in: -ωAsinφ/Acosφ = xi/vi tanφ = xi/(-ωvi) tanφ = 0.4 And here they (the textbook) got φ = 0.127π, This is where I...
  9. Clockclocle

    Compare the ratio of two times t1/t2 in this vertical jump

    Here is my attempt. At ymax the velocity turn to zero so we get time t*=v0/g and ymax=1/2 (v0^2/g). At the height y max, since the velocity at this point is 0, i get another equation y= 1/2(v0^2/g)-(g/2)t^2, this equation could be considered as continuation of first equation. Set ymax/2=1/4...
  10. binis

    I What is Earth's escape velocity?

    Since space is curved within the Earth's gravitational field, every body that moves there will follow the curvature of space no matter what speed it has, so what will its trajectory be, how will it be straight, only if the launch is made absolutely vertically towards sea level? Only then can it...
  11. srnixo

    Measuring the Velocity of Sound in this Lab Exercise

    Here is the exercise: Which one seems logical and correct ? this one: [ Normally when we increase distances, the velocity of sound decreases?] Or this one? You might wonder why. Well, my friend in class told me that the second table could be correct because the experiment was conducted at...
  12. D

    Projectile motion, initial height and range given, find initial velocity

    the answer to this question uses the above formula with the tangent function and solves for the initial velocity, i used the equation (v.sinθ^2) = (v.sinθ)^2 - 2gΔy, setting final velocity equal to zero and solving for initial velocity. this kinematic equation gives a different answer. can...
  13. C

    B Question about Morin's time dilation explanation

    Hello everyone, I'm reading Morins book which I like, and I feel I kind of understand the part on time dilation, however I'm a little confused by the geometry of the Pythagorian theorem when applied to velocities. On the moving clock he shows the velocity of light on the diagonal it traces...
  14. U

    I Rocket thrust equation -- What is velocity V in mass flow rate formula?

    What is velocity V in mass flow rate formula, velocity of inlet ,outlet, velocity of rocket speed in relation to freestream?
  15. M

    Vertical Velocity Graph versus Time on a Slope

    I understand that through process of elimination the only plausible solution is (E), but a question that rises up: When the ball bounces, does the velocity change from negative to positive instantly (as shown by the dotted lines) or gradually (a very small time period, but still solid line)?
  16. brotherbobby

    A particle moving in a parabolic path in the ##x-y## plane

    Problem statement : I copy and paste the problem as it appears in the text down below. I have only changed the symbol of the given acceleration from ##a\rightarrow a_0##, owing to its constancy. Attempt : I must admit that I could proceed very little. Given...
  17. brotherbobby

    B Kinematic equations ##\textbf{purely}## from graphs

    1. The first equation between velocity ##v## and time ##t## can be derived using the graph I have drawn for the purpose as shown on the right. Since acceleration ##a_0## is a constant, the graph of ##v-t## is a straight line. The slope of the line is ##\dfrac{v-v_0}{t} = a_0\Rightarrow \boxed{v...
  18. L

    Inner product between velocity and acceleration is zero (parametric)

    Hi, I am having problems with task b I then defined the velocity vector and the acceleration vector as follows ##dot{\textbf{r}}'(t) = \frac{1}{||\dot{\textbf{r}}(t)||} \left(\begin{array}{c} \dot{r_1}(t) \\ \dot{r_2}(t) \end{array}\right)## and ##ddot{\textbf{r}}'(t) =...
  19. cxza

    Is the Final Velocity of a Fly Impacted by an Elephant's Mass?

    My solution was that the final velocity of the fly is equal to the mass of the elephant divided by the mass of the fly, and then multiplies by the delta in the elephant's velocity. My teacher said it was the wrong answer and that the calculations are presumably pretty long
  20. J

    Derivation of angular velocity using the unit circle

    $$ \ ω = \frac{Δα}{Δt} \ $$
  21. brslagle

    Distance traveled when decreasing velocity

    dont know where to start. Other than it will take 5 seconds for v = 0m/s
  22. S

    B Launch of a rocket - its initial displacement and velocity

    so then when we model the velocity of the motion of a rocket (e.g., in a mathematics report), is it reasonable to assume that the initial velocity equals zero? I also apologise for my lack of information if I made a huge mistake in my question 🙏🏻
  23. Lotto

    Movement of the water level in the barrel - calculate its velocity, etc.

    Here is only my solution: ##A_1 \frac{\mathrm d h}{\mathrm d t}=-A_2\sqrt{2hg}##, so by integrating we get ##h(t)=\left(\sqrt{h_0}-\frac{A_2}{2A_1}\sqrt{2g} t\right)^2.## Setting ##h(T)=0## we get ##T=\frac{A_1}{A_2}\sqrt{\frac{2h_0}{g}}.## By doing the first time derivative of ##h## we...
  24. X

    Is My Understanding of Angular Momentum and Trigonometry Correct?

    First, I have always consider that the angular momentum equals to inertia times angular velocity, but that’s not the case from the options perpective, is my memory wrong, or is there something wrong with the options? Another, I think I need to figure out the angle it went through, I think it has...
  25. ahira

    Frames of Reference: Find the speed and heading of the airplane

    so far what i have gotten to is that 300/0.75 = 400km/h but I dont know how to draw the diagram for this
  26. Spooky123

    Using Momentum Principle to Find Ratio of Speeds?

    Given that the ions are initially at rest my initial velocity is 0. Therefore my Vavg is equal to vf/2 Using the formula Vavg = Change in positon/time, I can solve vf to be equal to 2r/t. Using the momentum principle, I get an equation of 2r/t = FnetT/12m -> Given that the mass of the ion is...
  27. MatinSAR

    In a constant acceleration motion, Is it possible to have constant speed?

    I think it's not possible. In 3D for constant acceleration we have : ##\vec v = \vec v_0 + \vec a t## It's a line in 3 dimension so velocity's magnitude(speed) is changing with time. I appreciate any better idea.
  28. A

    How do you calculate the terminal velocity of these two balls?

    TL;DR Summary: Almost as difficult as the Physics Olympics semi-finals or finals The coefficient of friction of the two arcs is the same.The radius of the ball is not taken into account.The roll of the ball is ignored.Can it be calculated or estimated quantitatively?The difficulty is estimated...
  29. E

    Questions about a spring-mass system hanging vertically

    1) a=0 and v=0 2) 0.7 m/s
  30. mazia

    Questions Regarding a Cat Going Up a Ramp

    EDIT: I've finally found the solution, so here's what I did. First, calculate Work using the equation: (F-mgsin(theta))*displacement, where F=the force being applied by the push, theta is the angle of the ramp, and displacement is the length of the ramp. Now that you have the value for work...
  31. H

    Change in momentum: Child jumping from a swing on a playground

    800 - (32 x 9.8) = 32v/0.18 where v = velocity this gives me v = 2.736 m/s The answer given, however, is 800 = 32v/0.18, i.e. v = 4.5 m/s The difference, of course, is the weight of the child. I don't understand why this is not allowed for in the net force acting on the child. Can someone put me...
  32. S

    Projectile Motion Problem: Kicking a soccer ball over a fence

    initial velocity y component is (cos30) * 20. t = 25m / ((cos30) * 20)m/s = 1.45 seconds d = vt + .5at^2 v= 20sin30 v= 10 , d= 10(1.45s) + .5(-9.8m/s^s)(1.45s)^2 d=4.2m 4.2-2.5 = +1.7m, so the ball will not hit the fence I need confirmation please
  33. verkamp

    Calculating relative velocity -- Jumping between two moving trains

    is it possible? I've given it quite some thought, and my conclusion was that it would be possible, cuz right after I jump, I'll still have the same velocity in the same direction as the running train?
  34. SwetS

    A How is eq. 1.5.3 written using three-vectors and how does it lead to eq. 1.5.4?

    I am going through https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf, here I don't understand how we wrote eq. 1.5.3 with the help of three-vectors to get eq. 1.5.4.
  35. yashboi123

    The velocity of a satellite rotating around the Earth

    Not sure what r would be in this scenario. I tried adding the radius of the earth to the altitude but that wasn't correct either.
  36. Lotto

    B What will be the ball's velocity after a perfectly elastic collision?

    From the bus driver's point of view, who is at rest, the ball's initial velocity is ##u+v##. After the collision, its velocity has to have the same value, but an opposite direction, so ##-(u+v)##. So that means that relative to me standing on the ground at rest, the ball's new velocity is...
  37. giodude

    8.01 MIT OCW PS1.4: Throw and Catch (Kinematics)

    1) Using "The person catches the ball at exactly the same height it was thrown from.", we can isolate t by solving yb(t) = v0*sin(theta)*t - (1/2)*g*(t^2) = 0: yb(t) = v0*sin(theta)*t - (1/2)*g*(t^2) = 0 v0*sin(theta)*t = (1/2)*g*(t^2) 2*v0*sin(theta) = g*t t = 2*v0*sin(theta) / g 2) At the...
  38. question_asker

    I Tracing parabolic motion with only current velocity and position?

    Is it possible to trace the trajectory of an object using only its velocity and position, both of which are given as components. My method of doing so involves using the time until max height is reached, and using that time value to calculate the max height itself (h,k), then plugging in the...
  39. S

    Speed of Message Relative to a Space Station: Relativistic Addition

    u is the speed of the message relative to the station v is the speed of the spaceship relative to the station u’ is the speed of the message relative to the spaceship u=(-0.5c+0.7c)/(1+((-0.5c)(0.7c))/c^2 ) =0.2c/0.65=0.308c This just seems way too high, and I'm not sure if I'm doing it...
  40. Slimy0233

    Velocity vs Speed (What's more relevant here?)

    This is a famous book in India. I was wondering if one could say if the answer should include velocity or speed. I mean, I don't think there are any details which hint at velocity. We are gives speed in the question and we are asked to find out the distance traveled, this hints we are asked to...
  41. Amsalja

    What is Velocity.length_squared?

    I'm not sure. A source said New Velocity = Current Velocity - TerminalVelocity every second until New Velocity = TerminalVelocity But it doesn't seem right
  42. Slimy0233

    Calculate Distance Traveled: Instantaneous vs. Average Velocity

    edit: I don't know why my latex isn't rendering, any help would be appreciated. Edit 2: The question was due to a misunderstanding I had, I thought integrating instantaneous velocity would give me average velocity. I have attached what I have tried so far. I had a doubt. Can you calculate the...
  43. J

    Velocity and the human experience

    TL;DR Summary: Velocity and the human experience As I was walking into work this morning I looked up and noticed an airplane flying overhead. Airplanes travel at speeds of up to 550 miles per hour while in flight. This question is really less about physics and more about our everyday...
  44. paulb203

    B Velocity of freefalling bodies after 1s, 2s, 3s, etc

    On many websites etc the velocity of a freefalling object in a vacuum is shown as follows. After 1,2,3 and 4 seconds respectively; 9.8m/s; 19.6m/s; 29.4m/s; 39.2m/s I worked out the distance travelled by a freefalling object in a vacuum using d = at^2/2, or, d = 0.5gt^2 and got, for after...
  45. M

    Moving Source, Observer at Rest, derivation for Doppler effect

    For this, Does someone please know whether they assume for the equation highlighted that ##\frac{v}{f} ≥ \frac{v_S}{f}## since otherwise the wavelength would be negative (which I assume is impossible)? Many thanks!
  46. H

    Circular Motion: Tangential and Normal Acceleration

    Hello Physicsforum! This is my attempt: First I realised: ##a_s=a_n## Secondly I used since previus known formulas: ##a_n=\frac {v^2} {R}## ##v=v_0+a_s*t## Although now I do not know how to continue, any suggestions would be appriciated! Thanks for your help on beforehand :smile:
  47. B

    Graphing velocity, acceleration, and position

    im not sure where to start
  48. P

    What is the velocity vector of (rsin(phi), rcos(phi), 1) ?

    I did try to solve the problem by forming the derivative and my result was: v=(rcos(phi), -rsin(phi),0). My solution is wrong, the tutor corrected the task but he didn’t give us the results. My question is what the solution is. Thanks in advance.
  49. A

    Why is the work done double its expected value? (conveyer belt)

    The question was this: My calculations show that the answer should be equal to work done on crate to make it reach the same velocity which is equal to 216 J but the answer given is 432 J It is believed that extra energy is needed to overcome friction but friction is an internal force and...
  50. BadgerBadger92

    B Perception of Velocity in Special Relativity

    If an object is going close to the speed of light, will outside frames of references perceive the moving object as going slow or fast?
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