Linked Questions
12 questions linked to/from Infinite series of derivatives of position when starting from rest
16
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3
answers
3k
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How does anything move? [duplicate]
So in order for two things $A$ and $B$ to move apart, for example, relative to each other, $B$ can be set into motion away from $A$. This means that we have to increase $B$'s velocity and therefore ...
-2
votes
2
answers
154
views
Apparent paradox of motion [duplicate]
I have what appears to be a paradox of motion, but it could just be my misunderstanding. It works under the assumptions that motion is fundamentally continuous, that position, velocity, acceleration ...
- 99
1
vote
2
answers
85
views
For regular moving objects around us, how many times can I differentiate their position with respect to time until I reach a constant? [duplicate]
When I practise problems, I come across ideal situations like constant velocities, constant accelerations, etc. But in real situations, objects usually don't magically gain momentum or acquire ...
- 385
0
votes
1
answer
177
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Acceleration as the second derivative of $e^{-\frac{1}{t^2}}$ [duplicate]
If we have, say, a material point with a zero velocity at the time $t=0$, and this point starts moving at a time $t>0$ , then we look at the force impressed on the point by inspecting the second ...
- 139
3
votes
1
answer
132
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Can a "flat function" be a particle trajectory? [duplicate]
Recently I came across the concept of a flat function, which is a smooth function $f:\mathbb{R}\to\mathbb{R}$ all of whose derivatives vanish at a given point $x_0\in\mathbb{R}$, the canonical example ...
- 761
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
50
votes
5
answers
10k
views
Norton's dome and its equation
Norton's dome is the curve $$h(r) = \frac{2}{3g} r ^{3/2}.$$ Where $h$ is the height and $r$ is radial arc distance along the dome. The top of the dome is at $h = 0$.
Via Norton's web.
If we put a ...
- 1,751
29
votes
1
answer
5k
views
What situations in classical physics are non-deterministic?
In Sean Carroll's book "The Big Picture," he states (chapter 4, page 35):
Classical mechanics, the system of equations studied by Newton and
Laplace, isn't perfectly deterministic. There are ...
- 3,566
4
votes
2
answers
616
views
Non-uniqueness of solutions in Newtonian mechanics
In The Variational Principles of Mechanics by Lanczos, in section 1 of Chapter 1, Lanczos states that for a complicated situation, the Newtonian approach fails to give a unique answer to the problem, ...
- 41
1
vote
3
answers
252
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Why does a particle initially at rest at origin with acceleration as square of its $x$ coordinate ever move?
Consider a particle initially at rest at origin, with acceleration, $a$, such that $ a(x)=x^2$.
Since the particle is at origin, initial acceleration would be 0. It's also at rest initially. Its $x$-...
- 371
0
votes
2
answers
490
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Acceleration with zero initial power?
Power = Force x velocity
At the initial instant, the velocity = 0, so the power is zero, even though there may be force, but zero power is taken from that force. So how can the object even start ...
- 1,956
0
votes
2
answers
113
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Is the motion of a particle non-analytic?
I really can't understand what happens during the time $t(0)$ to $t(0+dt)$ in the following crackpot arguement:
A particle is at rest (in an ideal frictionless world) until $t(0)$. So every order ...
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