All Questions
Tagged with differentiation velocity
105 questions
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Can we calculate centripetal acceleration by using this method $\frac{\mathbf v_2-\mathbf v_1}{T}$?
If we know the angle between two velocity vectors $\mathbf v_1$ and $\mathbf v_2$, and if we know the time $T$ it takes for the velocity to change from $\mathbf v_1$ to $\mathbf v_2$,then is it ...
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1
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D'Alembert's principle derivation in Goldstein's Classical Mechanics book [duplicate]
(I could not find any answer to the following question in other related questions posted on SE, so asking it here.)
In the derivation of D'Alembert's principle in his "book", Goldstein uses the ...
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3
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Can you use $a=$$\frac{\Delta v}{\Delta t}$ instead of $\frac{dv}{dt}$ to find instantaneous acceleration?
Can you use $\frac{\Delta v}{\Delta t}$ instead of $\frac{dv}{dt}$ to find instantaneous acceleration?
- 502
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2
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Velocity as a property
Is velocity considered to be a property like mass and weight that can be measured at a single moment in time, such as mass of X measured at time T1, or is it a property that needs to be measured over ...
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2
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220
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Average velocity and instantaneous velocity
In some books of Physics in Italian language, they write that the instantaneous velocity $v$, is:
$$v=\frac{dr}{dt}=\lim_{\Delta t \to 0} \frac{\Delta r}{\Delta t}$$
where $v_{\text{avg}}={\Delta r}/...
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Related to the information contained in $a = v \frac {dv}{ds}$
While studying kinematics I came to the definition of acceleration which is $a = \frac {dv}{dt}$. But from this equation we can derive that $ a = v \frac {dv}{ds} $ which when I evaluate at $v=0ms^{-1}...
user238497
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When the direction of a movement changes, is the object at rest at some time?
The question I asked was disputed amongst XVIIe century physicists (at least before the invention of calculus).
Reference: Spinoza, Principles of Descartes' philosophy ( Part II: Descartes' Physics, ...
user229097
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1
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Meaning of normal acceleration?
acceleration means the rate of change in velocity (vector quantity) and the differentiation means to divide a certain quantity into small elements (i.e $dx$) as we do to find the acceleration at any ...
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4
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Why the need for defining the velocity as a derivative? [closed]
Something intuitive and fundamental as the concept of velocity (of a particle for example) in classical physics is defined as a derivative, a concept to me quite vague and strange, although i know its ...
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How does instantaneous velocity or acceleration have any other numerical value than 0? [duplicate]
Instantaneous velocity is defined as the limit of average velocity as the time interval ∆t becomes infinitesimally small. Average velocity is defined as the change in position divided by the time ...
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Question about derivation of kinematics equations
Apologies if this has been asked before, but I browsed the sub and couldn't find something specific.
I understand the derivation for one of the equations as follows:
\begin{gather}
\frac{dv}{dt} = a ...
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2
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158
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What does it mean for velocity to be a derivative of position, if position a point, not a function? [closed]
So in mass-spring simulation I encountered that one simulates particles by using positions and velocities of particles etc.
People may say that velocity is the derivative of position.
But isn't "...
- 459
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A doubt regarding Modelling physical phenomena and position uncertainty
For example, in velocity, when we say $v=\frac{dx}{dt}$, there is no proof for it. Its almost like an axiom. Something taken to be true, without a proof. How do I know that for every $x=f(t)$, $v=f'(t)...
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What happens to velocity when Time equals zero?
I am not formally educated in Science but natural questions have always intrigued me.The way I put it is that I am married to Commerce but Science has been a childhood love. Now I have this very basic ...
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Speed is different when differentiating a function and when not differentiating
I have the function, $S(t) = t^2$.
When Finding speed $= V = \frac{dS}{dt}$, we get $V = 2t$.
Now If, I don't differentiate it and simply put
$V = \frac{Distance(S)}{Time(t)} = \frac{t^2}{t}$
We ...
2
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2
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Instantaneous velocity applications
I refered these two questions
Instantaneous velocity
How to interpret instantaneous velocity using limit?
and I understood how instantaneous velocity is defined. But why do we define it?
Velocity ...
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993
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Question about derivation of four-velocity vector
In order to describe a notion of rate of change of positon, in four-dimensional spacetime, we have to introduce the concept of four-velocity.
So, consider the following:
For a massive particle ...
- 3,159
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Confused with derivative and partial derivative
suppose $x=f(t)$ with a constant acceleration.
Then does $\frac{\text d x}{\text d t} = \frac{\partial (x)}{\partial(t)}$ since the position in $x$ only changes with time?
Then the acceleration in ...
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1
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240
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Why is velocity mathematically describes as a division? [duplicate]
I want to know why, in kinematics, is velocity described as $v = \frac{\Delta x}{\Delta t}$, and why it is not described as any other expression (like a multiplication), why does a division is the one ...
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With what velocity are we moving along the time dimension?
Does the question make sense? Velocity along time axis means $v_t=\mathrm dt/\mathrm dt$? If it doesn't, please explain where the flaw is. Taking time as measure like length? Or do we need to ...
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Why the acceleration is specified if I know the coordinates and velocity?
And I don’t understand why the acceleration can be specified if we know the coordinates and velocity
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Why isn't the Euler-Lagrange equation trivial?
The Euler-Lagrange equation gives the equations of motion of a system with Lagrangian $L$. Let $q^\alpha$ represent the generalized coordinates of a configuration manifold, $t$ represent time. The ...
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How is velocity defined in circular motion in central force field?
In my view the velocity is change of displacement in the increasing direction of displacement. Now in circular motion in central force field the particle is changing its direction then how is the ...
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Which relation is correct for resultant instantaneous velocity in 2d?
Please forgive me if the following question sounds silly and I can't exactly pin point where exactly the problem is but there is some problem with my understanding of vectors.
In Cartesian ...
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Assistance interpreting equation
Given a position function of a particle:
$$
\mathbf r=r\,\hat{\mathbf r}\left(\theta\right),
$$
where $\hat{\mathbf r}(θ)$ is the polar unit vector, to find the velocity, we take the derivative which ...
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2
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290
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Kinematics problem invloving position and time [closed]
An object is moving along X axis with position as a function of time given by $x = x(t)$. Point $O$ is at $x = 0$. The object is definitely moving towards $O$ when
1. $\mathrm dx/\mathrm dt < 0$
...
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2
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368
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How instantaneous speed is defined as magnitude of instant velocity? [closed]
Let $s=$distance (a variable)
we define instantaneous speed = magnitude $\left[\frac{ds}{dt}\right]$.
However instantaneous speed is also defined as magnitude of instantaneous velocity
i.e. ...
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7
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What's the difference between average velocity and instantaneous velocity?
Suppose the distance $x$ varies with time as:
$$x = 490t^2.$$
We have to calculate the velocity at $t = 10\ \mathrm s$.
My question is that why can't we just put $t = 10$ in the equation $$x = 490t^2$...
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1
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How to find Net Force with constant velocity? [closed]
Does having a constant velocity always make the acceleration equal zero?
For example: A 5 kg ball is moving at constant velocity of 15 m/s. What is the net force on the ball?
If the formula is $F_{...
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1
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How can there be instantaneous rate of change? [duplicate]
To find rate of change you need two instants.
how is the rate of change calculated at a particular instant when at least two instants are needed to find it?
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Velocity in generalized coordinates
Consider the expression of velocity in generalized coordinates, $\mathbf v = \frac {d \mathbf x}{dt}$, where $\mathbf x = \mathbf x (\mathbf q(t), t)$.
We end up with a total derivative, i.e $$\...
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Acceleration and velocity
I'm a freshmen student, I got this question in my mind why we consider acceleration based on velocity not speed.
as far as I know, velocity will be zero if we go and back from A to B although speed ...
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Hamilton's Formulation and Independent Coordinates
In Lagrange's formulation we know that $q,\dot {q}$ are independent of each other i.e,
$$\frac { \partial q }{ \partial \dot { q } } =0.$$
My question is, is this true for $p$, $q$ in Hamilton's ...
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Direction of velocity vector in 3D space
According to a well-known textbook (Halliday & Resnick), the direction of a velocity vector, $\vec v$, at any instant is the direction of the tangent to a particle's path at that instant, as is ...
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Why is $\vec{v}\cdot d \vec{v} = v dv$? [closed]
Can someone help me understand why is this true:
$$\vec{v} \cdot d \vec{v} = v \cdot dv$$
where $v$ is speed? I found somewhere that $\vec{v} \cdot d \vec{v}=|\vec{v}||d \vec{v}| \cos \phi$. And I ...
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Does differentiating a distance with respect to time give velocity?
I'm just wondering if you have a distance function:
$$
s(t) = 0.1t^2 - 5t
$$
where $s(t)$ is distance and $t$ is time in seconds, does differentiating it give you a function for velocity?
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Simple 2D motion vectors [closed]
I am curious if the initial velocity of $x(t)=-3-4t+2t^2$ can be calculated from only this given in another way than just differentiation, by using the constant acceleration formulas perhaps?
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For how long is an objects velocity it's instantaneous velocity at time $t$?
Basically I'm asking if an object's instantaneous velocity at time $t$ is $8m/s$ and its instantaneous velocity at time $t^+$ (idk latex, but basically the t + an infinitely small number) is $10m/s$, ...
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1
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Find out which coordinate changes at faster rate [closed]
Suppose we have a particle, which moves along a path (in x-y plane) and say its path is the curve, $ 12y = x^3 $ .
I need to find out which coordinate (x or y) changes at faster rate at any given ...
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Velocity time graph analysis: what does a concave downward $v$-$t$ curve mean?
This is a screenshot from the lecture about the analysis of various velocity-time graphs I was watching.
I understand that
the concavity of velocity-time graph will tell about the
increasing or ...
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Shouldn't instantaneous velocity be the limit as both the displacement and time approach zero?
This is how Feynman defines velocity:
\begin{equation*}
v=\lim_{\Delta t\to0}\frac{\Delta s}{\Delta t}=d{s}/d{t}.
\end{equation*}
However, as the time interval gets smaller, the corresponding ...
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2
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250
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Car Drag Strip Simulation [closed]
I have written an iPhone App for to our local drag strip.
I'm trying to write a physics based information and simulation page duplicating the time slip you receive when you make a pass at a 1/4 mile ...
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3
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How does instantaneous speed work for circular motion?
Why do we use the formula $\lim_{\delta t→0} \delta s/\delta t$ to get the instantaneous speed? Since speed is distance divided by time, what does the limit have to do with this? I have a very limited ...
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What is the physical interpretation of a differential equation? [closed]
I would like to learn more about differential equations and their interpretation. I know the derivation rules, but I fail big time in interpreting and understanding the functionality of them. For this,...
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Position vs time graph with constant acceleration
Wondering from the position vs time graph of an object moving with constant acceleration. How could you find the velocity? So the position vs time graph would be a parabola. I am thinking that the ...
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Can a particle have no instantaneous velocity at all points of the path taken but a finite average velocity?
I have a question on kinematics.
Say the path traced by a particle is given by a Koch curve or Koch snowflake.
Now consider the particle starts from some arbitrary point $A$ on the curve and ...
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3
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Difference between $|d{\bf r}|$ and $d|{\bf r}|$
What is the difference between $|d{\bf r}|$ and $d|{\bf r}|$ and why are both of them not always equal to each other?
My question might seem stupid to some and will probably get downvoted but I have ...
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How to find tangential/radial/angular velocity for motion in any curve? [closed]
Is the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction? If so why?
Please try to give a different explanation ...
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Can we say that the instantaneous velocity of an object is the displacement in zero time?
Can we say that the instantaneous velocity of an object is the displacement in zero time?
In the image above the instantaneous velocity of the object as change in time gets closer and closer to zero ...
user66452
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9
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Can velocity be an undefined quantity?
We have the image below displaying the uniform velocity by time-distance graph. At every point velocity is constant but what if distance and time both become zero as at origin in the graph is? The ...
user66452