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Why isn't tangential acceleration just always 0?

This is probably a very stupid question but I can't help me. Tangential acceleration is $\vec{a_t}=\frac{dv}{dt}\frac{\vec{v}}{v}=\frac{\vec{v} \cdot \vec{a}}{v} \frac{\vec{v}}{v}$. Since $\vec{a}$ is ...
Quaeram's user avatar
  • 15
1 vote
1 answer
80 views

On the derivation of the jerk term in tensor notation

The jerk vector $\mathbf{J}(t)$ may be (element-wise) written as $$J^{i} = \frac{d A^{i}}{d t} + \Gamma^{i}_{jk} A^{j}V^{k}~~~~(*).$$ However, I can't correctly get the second term of the RHS above. ...
user avatar
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,...
sunxd's user avatar
  • 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 $\frac{dt}{dx}$. ...
Novo's user avatar
  • 103
1 vote
2 answers
159 views

One object moves along the cycloid at a constant rate, how about its acceleration? [closed]

We know that the parametric equation: $$x=R(\theta+\sin(\theta))$$ $$y=-R(1+\cos(\theta))$$ and the constant velocity $c$. How do I prove that the acceleration of the object in the $y$ direction is ...
Joy's user avatar
  • 21
0 votes
1 answer
129 views

Why intuitively is the tangent vector the derivative of velocity of position with respect to their modulus?

When trying to find the tangential velocity, many textbooks define the tangent direction as one of the following: or Intuitively, why is the tangent vector the derivative of the position with ...
XXb8's user avatar
  • 849
-2 votes
1 answer
49 views

What does the derivative of tangent means? [closed]

While studying the circular motion I had to find the derivative of a tangent so I thought what the derivative of a tangent could probably mean since the derivative of position gives velocity. Or think ...
fdownnn's user avatar
0 votes
1 answer
60 views

A particle moves along the curve $y=mx^a + c$ with a constant speed $v$. Find the velocity at x=n (in $i cap, j cap$) and acceleration at x=n [closed]

A particle moves along the curve $y=mx^a + c$ with a constant speed $v$. Find the velocity at x=n (in $i cap, j cap$) and acceleration at x=n. I tried this question as: I found out the slope of curve ...
FastAndTheCurious's user avatar
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 ...
Hoor Tiku's user avatar
0 votes
1 answer
53 views

Differentiation/Integration [closed]

I am given $v=6-4x$ where $v$ is velocity and $x$ is position of the body. I am now asked to find displacement between $t=1.4$, distance covered from $t=1.4$, average velocity from $t=2.5$, average ...
FastAndTheCurious's user avatar
1 vote
3 answers
307 views

What does the derivative of unit vector of velocity with respect to time represent?

let an object move with a constant accelration a. in my book,the following derivatve is said to be non-constant(variable). $$\frac{d[\frac{v}{|v|}]}{dt}$$ what does this mean? as far as i can think,it ...
Karan's user avatar
  • 41
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 ...
barbatos233's user avatar
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}\\ ...
Sohaib Ali Alburihy's user avatar
1 vote
1 answer
458 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 ...
Lalit Tolani's user avatar
2 votes
3 answers
131 views

Is motion in infinitesimal interval is linear?

As a kind of thought experiment I tried to think if a motion (including circular motion), when divided into infinitesimal time intervals is always linear motion (whether each interval of the motion is ...
Idop11's user avatar
  • 121
-4 votes
1 answer
71 views

Given that $m \dot v \cdot v = 0$ , how is it equal to $m \frac{d}{dt} (v \cdot v)/2$? [closed]

While studying about scalar triple product in vector algebra, I stumbled upon the following question with the solution. I want know how is $m \dot v \cdot v $ = $m \frac{d}{dt} (v \cdot v)/2$?
Adi Anil's user avatar
0 votes
1 answer
78 views

Particle paths - the distance moved by a particle in a velocity field

This question is is context to particle paths. Particle paths are trajectories of a given particle in the velocity field: $$\boldsymbol{u}(\boldsymbol{x},t)$$ A particle location at position $\...
Jack Jack's user avatar
  • 187
2 votes
1 answer
291 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 (...
Sahil's user avatar
  • 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 ...
Joe's user avatar
  • 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 ...
khan Abdullah's user avatar
3 votes
2 answers
133 views

Is this notation inconsistent? If not, can some explain why not?

Im working through a textbook section on particle kinematics. An example given is relating vertical velocity to horizontal velocity and states: $y$ has a constant velocity of $10 \ \rm [m/s]$ $y=(0....
RoRo's user avatar
  • 31
0 votes
2 answers
71 views

Why quantities in physics are always talking about rates? [closed]

I get the idea that physics wishes to study changes to discover new rules. But why is everything related to rates? Acceleration,Velocity? Could we use something else apart from these? What can you ...
Shadman Sakib's user avatar
0 votes
2 answers
139 views

How do I find the unit vector for the tangent? [closed]

A body moves in the track from A to B to C and so on. The magnitude of the velocity in any given moment is $|\vec V|$=$t^3$$[m/s]$. The body arrives to point B at $t$$=$$2$$[s]$. The line in the draw ...
Yoxbox's user avatar
  • 3
0 votes
1 answer
225 views

The time derivative of a vector not defined in terms of the time variable $t$

Recently I got a question where I needed to determine the time derivative of a position vector. However, the vector didn’t have the variable $t$ but instead had $x$, $y$, and $z$ as its terms, so I ...
Andrew Norfield's user avatar
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 ...
Pascu22's user avatar
  • 23
4 votes
3 answers
2k views

What does "Just before" and "Just after" really mean in physics problems?

So I'm stuck in a dynamics problem that asks what is the acceleration of a body just after A, where A is the point that separates the motion of the body from a curvilinear path to projectile motion. ...
Normal_Vector's user avatar
3 votes
3 answers
653 views

Confusion about successive derivatives of position in circular motion

Suppose we define a unit vector $\vec r$ along radial direction for a particle in uniform circular motion at an angular frequency $\omega$. Then we can write: $$\vec r = \cos(\omega t)\hat i + \sin(\...
Prateek Mourya's user avatar
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 ...
Rasputin's user avatar
4 votes
2 answers
312 views

Force and Accleration

It's just a basic question I had when I was studying physics years back, So acceleration have two equations $$a=\frac{F}{m}$$ and $$a=\frac{\text{d}v}{\text{d}t}$$ So by the first equation, if I'm ...
Nimrod's user avatar
  • 171
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 ...
Brian's user avatar
  • 8,040
-3 votes
2 answers
308 views

If we divide the second equation of motion by time $t$, why don't we get the first equation of motion where has $1/2$ come from? [duplicate]

The first equation of motion is $v = u + at$. The second equation of motion is $s = ut + \frac{at^2}{2}$. If we divide the second equation of motion by time $t$, why don't we get the first equation of ...
Nikhil Sheoran's user avatar
2 votes
4 answers
667 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'...
KaceEnigma's user avatar
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 ...
Pedro's user avatar
  • 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 ...
Ahmod Ahmed's user avatar
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 ...
Nectac's user avatar
  • 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 ...
user avatar
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
Curious 's user avatar
0 votes
1 answer
468 views

Partial derivative of a 4-velocity

Trying to do some basic manipulations with 4-vectors and I have a question about the proper (no pun intended) approach. It's probably easiest if we look at a simple example. So let's define a 4-...
Metropolis's user avatar
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 ...
Roger Michealson's user avatar
0 votes
0 answers
152 views

Product rule for 4-vectors and derivation of 4-force form

In deriving the form for the 4-force in special relativity, we begin with $$\frac{d}{d\tau}p^{\alpha}=m\frac{d}{d\tau}u^{\alpha}=f^\alpha$$ where $\tau$ is the proper time, m is rest mass. Since $...
lilolalorphism's user avatar
1 vote
4 answers
3k views

What is proper time, proper velocity and proper acceleration?

I am trying to derive the relativistic rocket equations found here [(4),(5),(6),(7),(8)] but I do not understand proper time, proper velocity and proper acceleration. Define a point $P$ with ...
user572780's user avatar
1 vote
4 answers
58 views

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 ...
Abdullah Al Zami's user avatar
0 votes
1 answer
71 views

Derivative of four-vectors [closed]

I have to take the derivative of $(P+2k-2q)^2$ with respect to $k^{\alpha}$. What I am doing is writing $(P+2k-2q)^2=(P+2k-2q)^{\alpha}(P+2k-2q)_{\alpha}$ Then its derivative comes to be $2(P+2k-...
haider's user avatar
  • 1
0 votes
3 answers
511 views

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?
Zheer's user avatar
  • 502
0 votes
1 answer
87 views

What mean this momentum-derivative?

I'm working with quantum gravity. I have to make a Taylor-series. I got some help for this, but I have problem with understanding the formalism. So, I have the operator $A((P-p)^2)$, which needs to ...
Atka's user avatar
  • 3
0 votes
1 answer
347 views

Projectile motion - differentiating the equation of trajectory to find the maximum height

I have the equation of trajectory: $ y = x\tan \theta - {\displaystyle gx^2 \over \displaystyle2u^2\cos^2 \theta}$ I also know that the maximum height is given by: ${\displaystyle u^2 \over\...
Luna's user avatar
  • 13
0 votes
2 answers
299 views

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 ...
Miles Esfahani's user avatar
1 vote
2 answers
220 views

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}/...
Sebastiano's user avatar
  • 2,575
1 vote
2 answers
133 views

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}...
user avatar
11 votes
4 answers
3k views

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, ...
user avatar