# 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. ### I Escape velocity near a black hole: Newtonian or Special Relativity?

For a spherical body mass M and radius r, the escape velocity at the surface is ##\sqrt{\frac{2GM}{r}}##. At the surface, an object mass m has GPE ##-\frac{GMm}{r}## and 0 GPE at infinity. So ##\frac{GMm}{r}## KE must be converted to GPE which means the minimum take off speed must be...
2. ### B Stopping power of rifle slugs

As a child, one of my family friends was an 80 year old neighbor, Harry R. Caldwell, who had been a famous tiger hunter in his youth. He killed tigers and Kodiak bears with a .22 or .25 caliber high power load that some felt too small for big game. [edit: the claim about the bear is false...

11. ### Man pulling a boat along the water with a rope (from above on a steep bank)

Attempt : Let me copy and paste the question from the text alongside. Method 1 : I draw an image of the problem situation to the right. Boat B moves to the right pulled by a rope from the point O where the man is located. The angle the boat makes with the horizontal ##\alpha## changes with...
12. ### Theoretical velocities at different heights sliding down an inclined plane

At 3m: U = 3 x 9.8 x 80 = 2352J U at 6m = 6 x 9.8 x 80 = 4704J k = 1/2mv^2 (4704-2352)J = 1/2 (80) v^2 v = 7.67 m/s At 0m (bottom): U = 0 4704J = 1/2 (80) v^2 = 10.84 m/s Okay so what is bothering me here is just that my working doesn't take into account the...
13. ### A charge q approaching two stationary charges q1 and q2

I'm only confused about one part of this problem and that is setting up the conservation of energy equation. In the solution, they just wrote this: $$\frac{mv_o^2}{2} = - k \frac{q_1 q}{r} + k \frac{q_2 q}{l + r}$$ where ##r## represents the distance at which the force created by the negative...
14. ### Circular motion of a Weightless rod

I used law of conservation of energy to calculate (d theta/ dt)^2 (from:mgasin theta=1/2m(d theta/dt.a)^2+1/2mu^2(u is the velocity of the C ring at time=t)), but wasnt able to find u(velocity of C).Is there any relationship between the tangential velocity of B(d theta/dt.a) and velocity of C(u)...
15. ### Relationship between linear velocity and angular velocity

I find the velocity vector that is perpendicular to the radius which is v*cos(theta). Once I obtained the velocity that is perpendicular to the radius I used the equation : v = wr. But my answer seems to be wrong, the actual answer to this question is v = wr*cos(theta). Why?
16. ### B Direction of drift velocity vs direction of current

I've done internet searches on this. There doesn't seem to be any agreement. Is the direction of the drift velocity in a wire the same as the (conventional) current? [AI Chatbot reference deleted by the Mentors]
17. ### I What if one is in 1905 and debating foundational fundamentals?

Einstein's theories are accepted since 100+ years. Modern science built on it somehow provides a proof of truth of his theories but what if one is living when Einstein proposed his theories and debating its merit? Einstein did two things: 1. He declared velocity of light as invariant c for all...
18. ### I What Happens to Rotational Velocity When AC Part is Dropped?

In figure AO = OB = 4m. C is the midpoint of AO. The rod rotates with a velocity of 5 rad/s about the axis PQ. What will be the rotational velocity of the remaining rod if AC part is suddenly dropped from the rod? Assume that the mass of this uniform rod is M.
19. ### What distance will be covered before coming to stop?

Phew; back n forth on this anyway, my lines ... ##v_{1} = \dfrac{1000}{20} = 50## m/s in the first ##10## seconds. ##v_{2} = \dfrac{1000}{30} = \dfrac{100}{3} ##m/s in the first ##35## seconds. where ##v_1## and ##v_2## are the respective velocities in ##10s## and ##35s## respectively...
20. ### AC gaussmeter in static magnetic field

When you shake back and forth AC gaussmeter ,he significantly increase reading(magnetic field), because device is moved in Earth static magnetic field. Does his acceleration or velocity cause increase in reading and why he even increase reading if magnetic field from Earth is static and...

22. ### B Speed is distance multiplied by time -- Is this correct?

Hello, In this study https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9784821/, the distance the punch travelled from start to impact is 0.49 meters and the time taken from start of punch (that's it, they define the start of punch as the moment the elbow first start to extend) to impact is 0.1...
23. ### I Question Regarding Force Being Equal, Even Moving Upwards (if V=0)?

I understand based on the equation F = ma that if there is no acceleration, the forces on the object all balance out to 0 in all directions. What I don't get is for example, slowly lowering a heavy stone slab at a constant velocity v, and raising it way above my head as high as I can at a...
24. ### Resistance force changing the velocity of an object

Mentor note: Moved from a technical section, so is missing the homework template. A Body of mass 1kg moves with a uniform velocity of magnitude 12m/s, a resistance of force of magnitude 6x^2 (newton) where x is the displacement (meter) which the body travels under the action of the resistance...
25. ### I Freqeuncy of Matter Waves Approaches Infinity as Velocity Approaches c

I have heard that the phase velocity of matter waves can be represented as c^2/v. But if the wavelength of these matter waves goes to zero as momentum approaches infinity and v approaches c, then does this mean that the frequency of the matter waves approaches infinity, to give the matter wave a...
26. ### Drag Forces and Terminal Velocity

Teacher says Im wrong on both these questions. I have consulted with other teachers and they say im correct. What do you guys think? 3. As mass increases, so does terminal velocity. 5. Fnet = FDrag - Fg ma = FDrag - mg FDrag = 79(8) + 79(10) FDrag = 632 + 790 = 1422 N Teacher Comments 5...

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28. ### B Time and right angle traveling twins paradox

So in scenario in which two ships(A and B) are moving relative to each other, and towards each other; each ship will measure the other to have a velocity. Within special relativity no observer himself moves. Do you agree? If you agree, assume each of the above two ships sends out shuttle along...
29. ### Graph of viscous force and velocity

my answer was A but i dont understand because when the viscous force equals the weight speed becomes constant but why does the viscous force needs to be equal of weight? is it weight = viscous force? or speed = viscous force?
30. ### Find the initial velocity ##U##

Now in determining the initial velocity; in my understanding, if ##s=1.8## then we consider the stone's motion from the top to the ground. Why not consider ##s=3.6##, the total distance traveled by stone from start point ##t=0##? Is it possible to model equations from this point? The stone...
31. ### Find the value of ##T## and distance of particle in the first ##4## seconds

solution is here; I just need to understand this part ##14.7 = -14.7 =9.8T##... why initial velocity upwards is a negative value? or i am interpreting it wrongly. ........... In my reasoning, ##v=u+at## ##0=14.7 + (-9.8)t## ## t_1=1.5## in reverse direction, from top to start point ##T##...
32. ### A small disk and a bigger half disk

I need to find ##v_1## and I know what are the initial conditions: ##\theta(0)=\pi## and ##\dot{\theta}(0)=0##. Then what is ##v_1## and how to find it? Thanks!
33. ### Change in the kinetic energy of a car driving up a hill

part i) i did 1/2 * 1700 * v^2 i dont know what v is... so how do i solve it? part ii) i calculated it correctly by 440*25 please explain in detail why i used 440? and part d) i did 1.7*10^4 = 48000/t my t= 2.82 s but correct answer is 3.5s
34. ### Found PhysicForums while working on ballistics problem

Several different sites, including PhysicsForums, mention/discuss a formula for computing a bullet's Ballistic Coefficient based on measuring two downrange velocities where the measurements are made a distance L between them. This can be done with traditional skyscreen (optical) chronographs or...
35. ### I Why Does Differential Pressure Vary As The Square Of The Flow?

Can someone explain to me Bernoulli's principle as to why the pressure across a restriction varies as the square of the velocity? I'm looking for an understanding (conceptual) as to why this is without a gazillion math examples please. Thanks.
36. ### A The effect of perpendicular wind at channel inlet

Hello I'm thinking of how to attack this problem. Outside a channel-inlet, wind is passing perpendicular to the opening with a wind speed of 9 m/s and a fan sucks in a certain amount of air into this channel so that the velocity in the channel is 3 m/s. When the outside air is 0 m/s I have no...
37. ### Is this projectile motion situation possible?

Hi everyone, I have created a question which I thought would have a single simple solution, but have noticed there are two possible answers. This makes me think that the question's scenario is impossible with the numbers I made up. I think we all can agree that the horizontal component to...
38. ### B More convenient mathematical notation for a simple use case

So in my textbook there's a basic problem where you solve for the final velocities of two hockey pucks, which happen to have different colors which are red and blue, using conservation of momentum. The notation that the textbook uses to express the final velocities of the pucks is ##v_{1,f}##...
39. ### Find the distance a particle travels

My answer is d = (e+3)/e x(t) = ∫01 3t2 dt (0 ≤ t ≤1) = t3 |01 = 13 - 03 = 1m x(t) = ∫1∞ 3e-t dt (t > 1) = -3e-t |1∞ = lim(t->∞)[-3e-t] - [-3e-1] = 0 + 3e-1 = 3/e m Therefore total distance = 1m + 3/e m = (e+3)/e m However, the textbook answer gives...
40. ### 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...

42. ### 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×...
43. ### 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...
44. ### 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...
45. ### 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...
46. ### 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...
47. ### 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...
48. ### 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...
49. ### 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...
50. ### 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...