All Questions
Tagged with kinematics differentiation
191 questions
-2
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1
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58
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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 ...
-2
votes
0
answers
70
views
Use of $dv/ds$ in defining acceleration [duplicate]
We can write acceleration as either
$dv/dt$ or $v dv/ds$.
And surprisingly the work-energy theorem arrives from the second definition.
I feel it would be fundamentally understanding towards work ...
26
votes
21
answers
5k
views
What happens when a car starts moving? The last moment the car is at rest versus the first moment the car moves
Imagine a car that's at rest and then it starts moving. Consider these two moments:
The last moment the car is at rest.
The first moment the car moves.
The question is: what happens between these 2 ...
- 371
1
vote
1
answer
481
views
Doubt in Verlet's Algorithm
In studying the temporal evolution of a system according to the deterministic model, we begin by considering a Taylor series expansion for the displacement $r$. First, we consider a positive variation ...
- 123
0
votes
1
answer
90
views
Derivative of the product of a scalar function and a vector valued function
According to Berkeley Physics Course, Volume 1 Mechanics,
The time derivative of a vector valued function can be derived from the formula:
$$
\mathbf{r}(t) = r(t)\mathbf{\hat{r}}(t)
$$
where the ...
- 25
2
votes
1
answer
247
views
How to calculate jerk in uniform circular motion?
We can calculate the centripetal acceleration in circular motion by the equation v^2/r. But how do we calculate the jerk (which is acceleration over time)?
- 23
1
vote
1
answer
76
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How do force and mass work with all derivatives of position?
I think if $F(t) = kt^0$ then $$x(t) = x_0 + v_0t + \frac{k}{m}\frac{t^2}{2!},$$ and if $F(t) = kt^1$ then $$x(t) = x_0 + v_0t + \frac{k}{m} \frac{t^2}{2!} + \frac{k}{m} \frac{t^3}{3!},$$ and so on, ...
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0
votes
7
answers
104
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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
-1
votes
2
answers
80
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Problem with resources, Walter Lewin's third lecture
I've watched Walter's third lecture in 8.01 and I have a small problem with the last part, where he says that $$\vec r_t=x_t\cdot \hat x\ +\ y_t\cdot \hat y\ +\ z_t\cdot \hat z \\ \vec v_t=\frac{d\vec ...
0
votes
2
answers
89
views
How to calculate the final position of a particle under variable accelaration and its instantenous velocity?
I'm a first-semester physics student who was recently on a train. On a screen, it said the instantaneous velocity of the train was 176 km / h. We had 4 min left until our destination. I wanted to ...
- 127
0
votes
2
answers
84
views
Solving a PDE using $x-vt$ as a variable
So I was reading this Landau and Lifshitz paper:
https://doi.org/10.1016/B978-0-08-036364-6.50008-9
The article can also be found without a paywall by just searching its title, "On the Theory of ...
0
votes
1
answer
89
views
In $a = dv/dt$, is $a$ the net acceleration? [closed]
While going through the calculus approach to accelerate, we have,
$$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
-2
votes
3
answers
96
views
Why is it wrong to find centripetal acceleration using change of velocity over change of time?
This question asks to find the centripetal acceleration by giving the initial and final velocity over the change of time.
As shown, my book combined two rules to find the acceleration. I utterly ...
- 377
-2
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1
answer
91
views
From where does the expression of the tangential accerelation come from?
I've seen so many times that the expression of the tangential acceleration is known to be: $$a_t=\ddot{s}$$ but from the expression of the acceleration in spherical coordinates, in the tangential ...
- 69
0
votes
2
answers
42
views
Velocity to Acceleration negative line [closed]
Is the velocity line in below 0 is a different acceleration line?
For example from 0 - 6s and from 10 - 17s.
It has the same slope.
-2
votes
2
answers
122
views
Why does $\vec{a}=\vec{\omega}\times \vec{r}$ as well as the velocity does?
Today I came in class and in one of the problems the teacher used $\vec{a}=\vec{\omega}\times \vec{r}$ which made me very confused because I don't know where it comes from, it seems pulled out of thin ...
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1
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48
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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{...
-1
votes
1
answer
164
views
Given a Postion-time curve/function, how do I find the time spent per unit position?
I have recordings of the position time curve for a given 1D actuator.
I'm trying to find out the time spent per unit length.
To get this relationship, I tried to take an example of a linear function:
$...
- 57
1
vote
3
answers
231
views
Problem with the constant magnitude of vectors if the change in the same vector is perpendicular to it [duplicate]
Note: I am merely a highschool student attempting to self-study Classical Mechanics, some of the assumptions I make are perhaps wrong, so please bear with me. Thank you.
This while can be condensed ...
-2
votes
2
answers
113
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If an object is travelling at say 35 mps, if I somehow stop the time, is the speed zero or 35 mps? [closed]
I know we only go close to zero, not equal zero, but if that somehow happens, will it be zero as it is at rest or 35mps as when you resume the time, the speed is 35mps?
2
votes
4
answers
261
views
Show that $d\mathbf{v}^2/dt = 2\mathbf{v}\cdot d\mathbf{v}/dt$ using geometry only
I have just begun reading Modern Classical Physics by Thorne and Blandford and I am trying to wrap my head around their "geometric viewpoint" on classical mechanics. The first exercise in ...
- 510
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/...
3
votes
1
answer
79
views
What do we get on differentiating the instantaneous displacement function?
I was doing kinematics when a silly question came to my mind. It is as follows:
When we differentiate $x(t)$ (position as a function of time), we get $v(t)$ (instantaneous velocity). Doing the reverse,...
- 137
0
votes
3
answers
82
views
Chain rule when the intermediary variable might be equal to zero
I came across the following question in the kinematics section of my introductory physics textbook:
The velocity of a particle moving along x-axis is given as $v=x^2-5x+4$ (in $m/s$), where $x$ ...
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0
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0
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45
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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
0
votes
2
answers
414
views
Why does tangential acceleration become 0 when the velocity is max? [closed]
I know that tangential acceleration equal to zero when the circular motion is uniform, but why is it equal to zero, when the velocity is max or min? Because there is no relation between the value of ...
- 11
0
votes
1
answer
43
views
Are terms tangential acceleration and normal acceleration only used for instantaneous velocity?
Are terms tangential acceleration and normal acceleration only used
for instantaneous velocity?
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4
votes
6
answers
854
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 ...
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-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
2
votes
1
answer
172
views
How does instantaneous velocity cause displacement in just one point? [closed]
I have a question.
Falling object graph is curve shape right?
And instantaneous velocity is tangent line but how does this velocity make displacement in distance? Because suppose instantaneous ...
- 311
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
73
views
Why did my rearrangement with chain rule end up equating velocity to position?
We all know acceleration is the time-derivative of velocity which in turn is the time-derivative of position. Vice versa: position is the integration of velocity and velocity itself is the integration ...
- 401
1
vote
6
answers
113
views
If a body moves along a path (any path, not just circular) with constant speed, is it's tangential acceleration necessarily zero?
If a body moves along a path (any path, not just circular) with constant speed, is it's tangential acceleration necessarily zero?
I could only find general proofs for the case of circular motion and ...
0
votes
1
answer
100
views
How can a definite acceleration integral be useful in mechanics and why is an indefinite integral not used?
We have an acceleration function and in order to find the displacement function, it would be logical to take an indefinite integral 2 times. Then we would get a function. Why is it proposed here to ...
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1
vote
7
answers
293
views
I'm having trouble understanding the intuition behind why $a(x) = v\frac{\mathrm{d}v}{\mathrm{d}x}$ [duplicate]
I was shown
\begin{align}
a(x) &= \frac{\mathrm{d}v}{\mathrm{d}t}\\
&= \frac{\mathrm{d}v}{\mathrm{d}x}\underbrace{\frac{\mathrm{d}x}{\mathrm{d}t}}_{v}\\
&= v\frac{\mathrm{d}v}{\mathrm{d}x}
...
- 339
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
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1
answer
741
views
What are the relationships between the motion-time graphs?
I was wondering if someone could explain the relationships between the three motion graphs (Position-Time, Velocity-Time, and Acceleration-Time). I believe that the slope of the P-T is Velocity and ...
0
votes
2
answers
180
views
Why is the magnitude of velocity negative in this example?
Magnitudes are positive values, but when I take, for example: the magnitude of a position vector: $r = 3 - 0.04t^2$ and try to take the derivate of it, the result will be $v = -2 * 0.04t$ which is a ...
- 165
0
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1
answer
87
views
How do I reconcile these two definitions of acceleration?
How do I reconcile these two definitions of acceleration?
$$a=\frac{d\bar{v}}{dt}=(\frac{dv^k}{dt}+v^i v^j \Gamma^k_{ij})\bar{e}_k \tag{1}$$
and
$$a^k=v^{\small\beta} \nabla_{\small\beta} v^k.\tag{2}$$...
- 971
3
votes
2
answers
160
views
Acceleration in terms of displacement
I am having problems understanding the derivation of acceleration in terms of displacement. The first step is fine:
$$a(x) = \frac{\mathrm dv(x)}{\mathrm dt}
= \frac{\mathrm dv(x)}{\mathrm dx} \frac{\...
- 131
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
-4
votes
1
answer
97
views
Differentiation [closed]
Why is
$$\frac{d}{dt}v^2=2v\frac{dv}{dt},$$
When:
$$\frac{d}{dx}x^2=2x,$$
where $v$ is velocity? I don't understand why the variable $x^2$ has the derivative of $2x$, whereas the variable velocity has ...
0
votes
2
answers
678
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
0
votes
0
answers
42
views
In Radius of Curvature calculation why do I have to assume $\text{d}^2x/\text{d}t^2=0$?
Recently, I was calculating the radius of curvature of projectile trajectories at certain points. There are two ways to do the same:
Given the velocity and acceleration of the particle at some point, ...
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0
votes
4
answers
127
views
Standing Wave Equation: Why does assuming a small slope $du/dx$ not make $d^2u/dx^2$ negligible as well?
Referencing the above image, just change the label for $y$-axis to $u$-axis.^
Following the derivation of the standing wave equation: https://www.youtube.com/watch?v=IAut5Y-Ns7g&t=1324s
So if ...
- 719
1
vote
1
answer
94
views
Simple difference between module of velocity and time derivative of module of position [duplicate]
What is the conceptually difference between the two:
$$\frac{d|\vec{r}|}{dt}=\frac{\vec{r}\cdot\frac{d\vec{r}}{dt}}{|\vec{r}|}\neq|\dot{\vec{r}}|\equiv \bigg|\frac{d\vec{r}}{dt}\bigg|$$ ...
- 189
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
0
answers
55
views
What do you call $ \frac{d^2 r}{dt^2}$ in polar coordinates? [duplicate]
In polar coordinates, one finds centripetal acceleration as:
$$ a_c = \frac{d^2 r}{dt^2}- \frac{v^2}{r}$$
Where $|r|$ is distance from center to particle, $v$ is tangential velocity.
My question is ...
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