All Questions
Tagged with differentiation velocity
105 questions
-2
votes
1
answer
59
views
Need help in understanding Tangential Acceleration [closed]
I am studying Circular motion and I am confused about tangential acceleration and tangential velocity. I am studying uniform circular motion and it says the tangential acceleration is $0$ in uniform ...
9
votes
4
answers
4k
views
Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant but acceleration is constant?
Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant, but rate of change of velocity is constant?
Like speed is only the magnitude, so ...
0
votes
1
answer
69
views
Is 4-velocity a Vector in the Sense of Covariant Derivative along Worldline
The definition of 4-velocity $U^{\mu} \equiv dx^{\mu}(\tau)/d\tau$, however, we've learnt that the covariant derivative for a vector along a curve parametrized by proper time is,
$$\frac{DA^{\mu}}{D\...
- 938
0
votes
7
answers
104
views
How does the result of derivative become different from average ratio calculation?
Lets give an example. Velocity, $v=ds/dt$. If we know the value of $s$ (displacement) and $t$ (time), we can instantly find the value of $v$. But then this $v$ will be the average velocity.
Now ...
- 15
0
votes
2
answers
89
views
How to calculate the final position of a particle under variable accelaration and its instantenous velocity?
I'm a first-semester physics student who was recently on a train. On a screen, it said the instantaneous velocity of the train was 176 km / h. We had 4 min left until our destination. I wanted to ...
- 127
0
votes
1
answer
89
views
In $a = dv/dt$, is $a$ the net acceleration? [closed]
While going through the calculus approach to accelerate, we have,
$$a = dv/dt, $$
I think, here, v and a should be in the same axis,
is my process correct?
in a planar motion in two dimensions, it ...
- 1
1
vote
2
answers
142
views
Average velocity showing different results
I was solving a question, in which, a particle has travelled a distance $s$, with initial velocity $0$ and constant acceleration.
So the equation of motion becomes,
$$ v = a t \tag{1} $$
and
$$ v = \...
- 56
0
votes
1
answer
48
views
In circular motion is acceleration vector and $\frac{dv}{dt}$ the same?
I was studying a book in which they have written this
$$ a = -w^{2} r \hat{e} + \frac{dv
}{dt} \ddot{e} \tag{1} \label{1}$$
Where $a$ is acceleration vector $\hat{e}$ is unit radial vector and $\ddot{...
2
votes
3
answers
198
views
What is the definition of velocity?
We know that displacement is change in an object's position (here position means 'position vector'). Then velocity will be change in position of the object with respect to time, simply displacement/...
0
votes
0
answers
45
views
Physical and Diagrammatic representation of $a$=undefined when $v$=0 according to $a$=$vdv$/$dx$
$a$=acceleration
$v$=velocity
$x$=position along x axis
$t$=time instant
My teacher derived the $a$=$v$$dv$/$dx$ formula as follows
Assume a particle at time $t$ is at $x$ position having $v$ velocity
...
- 31
4
votes
6
answers
855
views
How to understand instantaneous velocity concept [duplicate]
When I started learning instantaneous velocity it didn't make sense to me. I don't understand in real life why we can't measure instantaneous velocity and therefore why we use this concept.
Or is this ...
- 311
-1
votes
2
answers
67
views
Instantanous and uniform velocity and acceleration [closed]
If the mathemical expression of instantanous velocity is $d/t$, what is the mathematical expression of uniform velocity.
If the mathematical expression of instantanous acceleration is $v/t$, what is ...
- 107
1
vote
0
answers
93
views
Does car move when instantaneous velocity is zero? [duplicate]
In 3blue1brown: derivative paradox.
supposed car moving with:
$S(t) = t^3$
And velocity is:
$V(t) = 3t^2$
He asked when t = 0 velocity is 0 m/s , does that car move at that time ?
And here his ...
- 311
0
votes
1
answer
72
views
Sine and Cosine Functions [closed]
So long story short, We were given a windmill to experiment with and a sensor could sense the Voltage produced and graph it concerning time. We decided to make a sine wave out of the positive and ...
1
vote
3
answers
95
views
What is the rate of change of time wrt velocity of an object?
disclaimer, I'm just an average highschooler so please be a little friendly with the mathematics of your answers but I wondered what would be $dt/dv$?
- 33
0
votes
6
answers
260
views
Why is force not dependent upon velocity but on acceleration?
Force is not dependent upon velocity but on acceleration but acceleration is dependent upon velocity, What i mean is a=change in velocity/change in time.So in order to calculate acceleration i need ...
- 79
1
vote
1
answer
1k
views
What does divergence of scalar times vector vector field physically mean?
We know that:
$\nabla \cdot (f \vec{A}) = f \nabla \cdot \vec{A} + \vec{A}\cdot(\nabla f)$
Now divergence of any vector field can be understood in terms of whether the concerning flux is outgoing ($\...
- 15
3
votes
2
answers
267
views
What does $\dot x$ mean as an operator in quantum mechanics?
I've been looking at a paper titled "Feynman's proof of the Maxwell Equations" by Freeman Dyson (American Journal of Physics 58, 209 (1990); https://doi.org/10.1119/1.16188) and I'm confused ...
- 41
2
votes
1
answer
435
views
When exactly does velocity increase or decrease on an acceleration time graph? [closed]
How does the acceleration time graph show if and object is speeding up or slowing down?
Is it possible to find the answer without any deep calculations? If yes then how?
Like how can I find the ...
- 137
0
votes
2
answers
679
views
Why is instantaneous velocity tangent to trajectory?
Trajectory is the path of an object through space as a function of time. However, in many trajectory plots, when the movement is planar, a horizontal position axis and a vertical position axis are ...
- 181
10
votes
7
answers
1k
views
What is the instant velocity? [duplicate]
The velocity is the variation rate of the position correct? So does it make sense to talk about velocity without time?
- 117
0
votes
1
answer
134
views
Velocities - Equation 1.46 of Goldstein 3rd edition
In his derivation of the Euler-Lagrange equations from D'Alembert's principle, Goldstein
uses the parametrization (equation 1.45')
$$\displaystyle{\vec{r_i}=\vec{r_i}(q_1,q_2, ..., q_n, t)}\tag{1.45'}$...
- 113
0
votes
3
answers
1k
views
Velocity gradient in a liquid
When we consider the motion of fluid in terms of many thin layers sliding over each other , we say that layer at a top of a layer forces it to move forward while layer below a layer forces it to move ...
- 892
0
votes
0
answers
85
views
Cartesian coordinate velocity and generalized coordinate velocity
use $x_k$ to denote the kth component of cartesian coordinate, and $q_k$ to denote the generalized coordinate.
Taking the derivate of $x_k(q_1,q_2,q_3,t)$ w.r.t. time, we have
$$\frac{d x_k(q_1,q_2,...
- 105
0
votes
0
answers
46
views
1/velocity for higher dimensions
I have a somewhat basic question. I am sorry if it trivial.
Denote the velocity by $v=\frac{dx}{dt}$ suppose that $x \in \mathbb{R}^n$ and I want to parametrize $t$ in $x$ and compute $\frac{dt}{dx}$. ...
- 103
1
vote
2
answers
319
views
What is the time derivative of the linear velocity vector $\vec{v}\,(t)$?
If $\vec{v}\,(t)$ denotes linear velocity, we can then write $\vec{v}\,(t)$ as $|v(t)|\hat{v}$. My question is what is $\displaystyle\frac{d\vec{v}\,(t)}{dt}?$
The answer I have seen to this question ...
- 39
0
votes
1
answer
42
views
Is such a situation realistically possible where $v$-$t$ graph is continuous but $a$-$t$ graph is not?
Taking for example $v = \cos(t-1)$ from $t \in [0,1]$ and $v = e^{t-1}$ from $t \in (1,\infty)$ and $t \ge 0$. At $t = 1$, the function shifts from cosine to exponential, but remains continuous since ...
1
vote
3
answers
647
views
Derivative as a fraction in deriving the Lorentz transformation for velocity
Consider a frame $S$ and $S'$ which is coincides at $t=0$ and then $S'$ starts moving with velocity $v$ in $+x$ direction.
By Lorentz transformation equation,
\begin{align}
x'&=\gamma(x-vt) \\
...
- 446
3
votes
3
answers
296
views
If the displacement of an object is not differentiable at some point, say $x(t)=t\sin(1/t)$ at $t=0$, how is its instant $v$ defined? [closed]
If instant velocity at any given time $t_0$ is defined as the derivative of $x(t)$ at $t_0$, what if the derivative does not exist? How are we supposed to deal with $x(t)=|t|$ at $t=0$, or for more ...
- 39
3
votes
2
answers
233
views
Generalization of straight line motion under constant acceleration
My question is that, we all know the three equations of straight line motion under constant acceleration,
\begin{align}
x & =x_{\rm o}+v_{\rm o}\,t+\tfrac12 \mathrm a\,t^2
\tag{1d-a}\label{1d-a}\\
...
1
vote
1
answer
459
views
Expressing acceleration in terms of velocity and derivative of velocity with respect to position
we know that
$$a = \dfrac{dv}{dt}$$
dividing numerator and denominator by $dx$, we get $$a=v\dfrac{dv}{dx}$$ provided that $dx$ is not equal to zero or instantaneous velocity not equal to zero
when I ...
- 892
2
votes
1
answer
292
views
Is the relation "slope=velocity" mathematically valid?
$\text{Slope= tan(angle with respect to positive X-axis)= scalar output}$
$\text{velocity= a vector }$
Source: Hugh D Young_ Roger A Freedman - University Physics with Modern Physics In SI Units (...
- 439
2
votes
1
answer
267
views
Is there a difference between instantaneous speed and the magnitude of instantaneous velocity?
Consider a particle that moves around the coordinate grid. After $t$ seconds, it has the position
$$
S(t)=(\cos t, \sin t) \quad 0 \leq t \leq \pi/2 \, .
$$
The particle traces a quarter arc of ...
- 131
3
votes
1
answer
4k
views
What is the meaning of word 'rate' in physics?
Often, I have seen in physics the rate of change of velocity or something like that in kinematics. And in question based on speed, time and distance. I would like to know the meaning of the word rate ...
2
votes
1
answer
203
views
Time derivative with respect to an observer moving with velocity $\mathbf{v}$
I am taking a class in fluid mechanics right now and my book has this statement with no explanation:
What is the time derivate seen by an observer moving with a velocity $\mathbf{v}$ of a scalar ...
- 707
1
vote
1
answer
347
views
Time derivative of $\rm{atan2}$ when $x=0$
I want to take the time derivative of the $\rm{atan2}$ function to calculate an azimuth rate in spherical coordinates, given position and velocity in Cartesian $xyz$ coordinates.
$$\rm{atan2}(y, x) =
\...
- 206
1
vote
1
answer
172
views
$dT/dx=0$ always true?
In a Classical Mechanics book I found the assumption that for an arbitrary particle with constant mass in the Real line $dT/dx=0$, with T the Kinetic Energy i.e. $T=(m·\dot x^2)/2$
My hypothesis is ...
- 145
2
votes
3
answers
193
views
Is $ d \mathbf v · d \mathbf v = d \mathit v^2 $?
My teacher has proved the following:
$$ \mathit v^2 = \mathbf v·\mathbf v = \frac{d\mathbf r}{dt}·\frac{d\mathbf r}{dt} = \left(\frac {ds}{dt}\right)^2 \Rightarrow \mathit v = \frac{ds}{dt} $$
Because ...
- 23
2
votes
5
answers
346
views
Significance of $\frac{dv}{dx}=0$
Suppose an object is moving with varying acceleration in time.
What does it mean when it hits a point where $\frac{dv}{dx}=0$?
Does it mean the object has hit maximum velocity?
Assume the object ...
- 77
34
votes
7
answers
5k
views
The usage of chain rule in physics
I often see in physics that, we say that we can multiply infinitesimals to use chain rule. For example,
$$ \frac{dv}{dt} = \frac{dv}{dx} \cdot v(t)$$
But, what bothers me about this is that it raises ...
- 8,040
4
votes
4
answers
413
views
Suppose there is a vector $\vec v$ which is a function of time, then will $\dfrac{d}{dt}|\vec v|$ be a vector quantity or a scalar quantity?
Suppose there is a vector $\vec v$ which is a function of time, then will $\dfrac{d}{dt}|\vec v|$ be a vector quantity or a scalar quantity?
I think it should be scalar because, let's assume $\vec v=...
- 223
2
votes
4
answers
668
views
Interpretation of Velocity as a time derivative of position
Going by the Wikipedia explanation, a derivative measures the 'sensitivity' of a function to tiny nudges in its input.
How well does this fit with the velocity being the derivative of position? I can'...
- 129
1
vote
2
answers
167
views
Velocity and acceleration in special relativity
I would like to compute what the constant acceleration trajectories are in the Minkowski spacetime $(t, x)$ with $d\tau^2 = dt^2 - dx^2$. So given some trajectory $x(t)$ I know the velocity vector is ...
- 592
1
vote
5
answers
385
views
A Problem with velocity vector
I am having a conceptual problem. I understand why the definition of the velocity of a body moving in one dimension is the derivate of its position coordinate. But I don't get why the velocity vector ...
- 13
0
votes
3
answers
232
views
Are acceleration and velocity simultaneous? [closed]
I would think yes because, if a rope tied to a swinging rock breaks, the rock flies off in the direction that is perpendicular to the direction of the last instant of the acceleration. The ...
- 71
0
votes
1
answer
88
views
Does "$\rm m/s$" mean the same thing when used for instantaneous velocity and for mean velocity?
The following question on Philosophy SE https://philosophy.stackexchange.com/q/73366/ relies on this "given"
"suppose that the instantaneous velocity of object A is $1$m/s and that the mean ...
user232501
1
vote
2
answers
557
views
In the equation: $a = dv/dt$ , is $dt$ the time taken to achieve that instantaneous acceleration?
If you solve for $dt$ from $a = \frac{dv}{dt}$ , is it the time taken to to achieved that instantaneous acceleration?
$a$ : acceleration
$v$ : velocity
$t$ : time
- 87
0
votes
3
answers
295
views
What does the first derivative of (2-norm) distance with respect to time tell us?
My basic physics' knowledge is a little rusty. My apologies in advance. I know that the first derivative of position or displacement with respect to time is the instantaneous velocity. Suppose I have ...
0
votes
1
answer
90
views
When the rate of acceleration changes it's sign how does the velocity change?
When the rate of acceleration changes its sign how does the velocity change? When another derivative of distance with respect to time is increased how does it affect factors like displacement and ...
- 39
9
votes
4
answers
2k
views
Can I find the acceleration or velocity when my displacement-time graph is discontinuous?
Today, I encountered the problem where I was asked to find the velocity and acceleration from displacement-time graph but the displacement-time graph was discontinuous. So I am unable to find the ...
- 123