All Questions
Tagged with calculus newtonian-mechanics
119
questions
5
votes
2
answers
3k
views
Why dont you take derivative of force in definition of power ? P=F.v
The derivative of work is $\bf F\cdot v .$
$$P(t)= \frac{\mathrm dW}{\mathrm dt}= \mathbf{F\cdot v}=-\frac{\mathrm dU}{\mathrm dt}\;.$$
But why not $$\frac{\mathrm{d}\mathbf{F}}{\mathrm{d}t}\cdot \...
- 115
1
vote
1
answer
124
views
How to model terminal velocity as a function of gravitational acceleration?
Taking the most simplistic form of terminal velocity, $v=\sqrt{\frac{mg}{c}}$
I want to try and derive an equation that models the velocity as g changes in height.. Because obviously the terminal ...
- 546
0
votes
2
answers
5k
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Can you take the integral of $ d^2x\over dt^2$? [closed]
I am messing around with physics problems, and as silly as this maybe how do you take the integral of
$$\int_0^\infty xd^2x$$
For example taking Newton's Second law $F=ma$
$$
F=m{d^2x\over dt^2}
$$...
- 546
-2
votes
2
answers
103
views
Find $\oint xdx+2ydy+3zdz$ on the line segment formed by points $A(1,0,-1)$,$B(2,5,-1)$ [closed]
Find $\oint xdx+2ydy+3zdz$ on the line segment formed by points $A(1,0,-1)$,$B(2,5,-1)$
My approach:
First I find the line segment formed by $A,B$ which is $\vec l(t)=\vec{OA}+t\vec{AB}=(1,0,-1)+t(1,...
- 107
0
votes
2
answers
221
views
Differentiating displacement with respect to speed in order to obtain time
I have this problem where I am trying to calculate $d(t)$ and $v(t)$ of a mass m on a spring, dropped from a displacement $A$, without using anything else than Hooke's law and energy calculations. ...
- 75
3
votes
2
answers
2k
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Falling rain drop problem [closed]
EDIT: I've read that a ball moving in a rectilinear motion with a non-constant radio, $r$ satisfies that
$$\frac{dV_c}{dy} = \pi r^2,$$
where $V_c$ is the volume swept by the ball and $y$ is the ...
- 160
0
votes
1
answer
81
views
Confusion regarding area from graph
This might be a trivial question but is illustrated below.
Why is the area 'below' the graph always taken for a velocity-time graph when finding the displacement? I mean why is the area with the time ...
- 51
24
votes
7
answers
12k
views
Zero velocity, zero acceleration?
In one dimension, the acceleration of a particle can be written as:
$$a = \frac{dv}{dt} = \frac{dv}{dx} \frac{dx}{dt} = v \frac{dv}{dx}$$
Does this equation imply that if:
$$v = 0$$
Then,
$$\...
- 383
0
votes
2
answers
304
views
Is the Fundamental Theorem of Calculus really applicable to the definition of work?
When the force $F$ on an object is not constant, then the work it performs is defined as $$W = \int_{x_0}^{x} F(X)dX.$$
Now, the Fundamental Theorem of Calculus states that
$$\text{If}\,\,\, f(x) =...
user36790
1
vote
3
answers
169
views
Integral ambiguity
I'm a bit confused with some notation I encounter in physics calculus. Consider this:
Taken from here.
Integration operates on functions, correct? What does it mean to integrate $\frac{d{\bf p}}{dt} ...
2
votes
1
answer
1k
views
Taylor series expansion of $\ln$ and $\cosh$ in distance fallen in time $t$ equation
I want to find the Taylor expansion of $y=\frac {V_t^2}{g} \ln(\cosh(\frac{gt}{V_t}))$
I have tried using the fact $\cosh x= \frac {e^x}{2}$ for large t, which works, I just need help on small values ...
- 345
0
votes
1
answer
667
views
Investigation of a pendulum's period, problem creating equation to sum the dynamic velocity
I am investigating the period of a pendulum swing. This is a simple harmonic pendulum and I am already aware of the common, but slightly inaccurate,
$2\pi \sqrt{\frac{L}{G}}$ formula.
My problem is ...
- 1,229
9
votes
6
answers
2k
views
Is Newton's first law something real or a mathematical formalism?
Why do objects always 'tend' to move in straight lines? How come, everytime I see a curved path that an object takes, I can always say that the object tends to move in a straight line over 'small' ...
- 309
1
vote
2
answers
158
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Showing $ m\int \frac{d\textbf{v}}{dt} \dot \normalsize \textbf{v}dt = \frac{m}{2}\int \frac{d(v^2)}{dt}{}dt$
Can someone please explain how this equation is valid, using intermediate steps if available?
$$ m\int \frac{d\textbf{v}}{dt} \dot \normalsize \textbf{v}dt = \frac{m}{2}\int \frac{d(v^2)}{dt}{}dt$$
...
- 2,251