All Questions
Tagged with kinematics differentiation
23 questions
10
votes
6
answers
3k
views
Physical intuition for higher order derivatives
Could somebody give me an intuitive physical interpretation of higher order derivatives (from 2 and so on), that is not related to position - velocity - acceleration - jerk - etc?
- 202
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 ...
- 8,040
5
votes
4
answers
5k
views
How can there be really any instantaneous velocity?
I have read about Zeno's arrow paradox that tells us there is no motion of the arrow at a particular instant of its flight. It can be inferred that there can be no velocity at any instant. Moreover we ...
user36790
4
votes
2
answers
293
views
Do integrals of position make any sense? Do they have an application? [closed]
I know that taking the derivative of position with respect to time defines what we call velocity, but I've never heard of physicist going in the opposite direction with position. Is there any ...
- 41
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
17
votes
7
answers
6k
views
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 $$x = 490t^2$...
3
votes
9
answers
4k
views
Can velocity be an undefined quantity?
We have the image below displaying the uniform velocity by time-distance graph. At every point velocity is constant but what if distance and time both become zero as at origin in the graph is? The ...
user66452
2
votes
1
answer
172
views
How does instantaneous velocity cause displacement in just one point? [closed]
I have a question.
Falling object graph is curve shape right?
And instantaneous velocity is tangent line but how does this velocity make displacement in distance? Because suppose instantaneous ...
- 311
1
vote
4
answers
3k
views
What is proper time, proper velocity and proper acceleration?
I am trying to derive the relativistic rocket equations found here [(4),(5),(6),(7),(8)] but I do not understand proper time, proper velocity and proper acceleration.
Define a point $P$ with ...
- 201
1
vote
4
answers
4k
views
Area under and slope of the motion graphs
I wanted to ask in general what area under the graph means. Also which physical quantity is highlighted by area under distance vs time graph.
I'm confused that area is a 2 dimensional concept and it ...
- 1,157
13
votes
7
answers
3k
views
Can we divide a vector by another vector? How about this: $a = vdv/dx?$
My physics teacher told us that we can’t divide vectors, that vector division has no physical meaning or significance. How about this: $$a = vdv/dx.$$
It says acceleration vector equals velocity (as ...
- 876
6
votes
3
answers
1k
views
Is $\dfrac{dx}{dt}$ a fraction or not?
I am new to calculus and during my mathematics class my sir defined $\dfrac{dx}{dt}$ as $$dx/dt=\lim_{t\to t_1}\dfrac{f(t)-f(t_1)}{t-t_1}$$ and my sir made a clear statement that
$\dfrac{dx}{dt}$ ...
- 480
6
votes
2
answers
1k
views
Terminology for time derivative of speed (not velocity)
Is there any standard terminology for the derivative of the magnitude of velocity with respect to time (suitable for use in first-year Calculus)? The word ‘acceleration’, in its technical sense, is ...
- 201
4
votes
6
answers
854
views
How to understand instantaneous velocity concept [duplicate]
When I started learning instantaneous velocity it didn't make sense to me. I don't understand in real life why we can't measure instantaneous velocity and therefore why we use this concept.
Or is this ...
- 311
2
votes
1
answer
267
views
Is there a difference between instantaneous speed and the magnitude of instantaneous velocity?
Consider a particle that moves around the coordinate grid. After $t$ seconds, it has the position
$$
S(t)=(\cos t, \sin t) \quad 0 \leq t \leq \pi/2 \, .
$$
The particle traces a quarter arc of ...
- 131
2
votes
4
answers
20k
views
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 ...
- 188
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
1
vote
5
answers
7k
views
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 ...
- 113
1
vote
2
answers
2k
views
If change in position over time is average velocity, why doesn't change in position over time squared equal average acceleration?
For example, let's say a car is experiencing an acceleration of $1$m/s$^2$, for $6$ seconds so it goes $18$m. Now the average velocity is found through dividing $18$m by $6$s which is in line with the ...
- 1,187
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 ...
- 71
0
votes
2
answers
993
views
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
0
votes
3
answers
2k
views
How to derive kinematics equations using calculus? [closed]
I read derivation of kinematics equations using calculus:
$$a=\frac{\text dv}{\text dt}$$
$$\implies \text dv=a\text dt$$
$$\implies \int_{v_0}^v\text dv=\int_0^t a\text dt$$
$$\implies v-v_0=at$$
$$\...
- 259
0
votes
7
answers
4k
views
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 ...
