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.
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...
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...
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...
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...
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?
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"
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?
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}}##...
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...
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.
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.
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...
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...
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
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}...
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...
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...
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...
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...
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...
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...
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 =...
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...
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...
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...
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?
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...
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...
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...
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...
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
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?
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...