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.
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...
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...
I was taught to solve this problem by first finding the velocity of the body (of mass ##m ##) relative to the block of mass ##M ##. One way of doing this is as follows: first write $$ {v _{m _{B }}}^{2 }={v _{mx _{B }}}^{2 }+{v _{my }}^{2 } (I)...
Hi, I have two topics:
1) Suppose a propeller is spinning very fast (say it's in a vacuum, no drag) and we arbitrarily lengthen its blades. Eventually the velocity of the tips of the propeller will approach the speed of light. That should be a speed limit, but that implies that the blades of...
Using equation, Vm=(Vo+Vi)/2;
2= (4+Vi)/2
=>Vi=0.
I.e, image velocity is zero.
I can't understand how it is possible that the image is at rest wrt ground. If the object moves with more velocity than the mirror, wouldn't it collide with the mirror at some point? And plus the object is moving 2m/s...
Lets just say for the sake of argument that the earth, sun, solar system, galaxy were all moving due north at 1,000,000 miles an hour. If you were to travel due south at 1,000,000 mph you would basically be not moving at all. How would this affect time for you or anyone observing you?
I would like to discuss a few ways to apply derivatives in physics (I don't understand it fully). I don't need a full solution, I only need to understand how to successfully apply the derivatives
First example,
Thin insulating ring of mass M, uniformly charged by charge ##+q## has a small cut...
According to the problem statement: $$a = \frac{dv}{dt} = const \implies dt = \frac{dv}{a} \implies \int_{0}^{T} \,dt = \frac{1}{a} \int_{0}^{v_f} \,dv \implies T = \frac{v_f}{a}$$ Now, the distance covered is given by, $$L = \int_{0}^{T} v \,dt \implies L = \frac{1}{a} \int_{0}^{v_f} v \,dv...
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...
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...
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...
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)...
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?
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]
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...
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.
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...
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...
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...
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...
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...
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...
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...
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...
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?
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...
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##...
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!
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
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...
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.
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...
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...
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}##...
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...
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...
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...
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...
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...
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...
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...
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...
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...