All Questions
Tagged with kinematics differentiation
191 questions
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
votes
1
answer
61
views
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?
- 1
-1
votes
2
answers
89
views
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 $10m/s$, ...
0
votes
4
answers
5k
views
Sign of acceleration from position-time graph
These three graphs are from my textbook. It states that the acceleration in 1) is positive, 2) is negative and 3) is zero and can be told by looking at the slope.
What I understand from the graph is ...
- 493
-4
votes
1
answer
74
views
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 ...
- 193
1
vote
2
answers
3k
views
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 ...
- 646
0
votes
1
answer
108
views
Acceleration varies inversely with 3rd power of displacement
Question. A particle is moving in a straight line. Displacement $x$ and time $t$ of the particle are related by the equation
$$x^2=at^2+2bt+c~;~\text{where }a,b,c\text{ are constants.}$$
Prove ...
1
vote
3
answers
2k
views
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 ...
- 341
4
votes
2
answers
861
views
Integration of tangential acceleration with respect to time
Here, by tangential acceleration, I mean the component of acceleration along the velocity vector.
What do you get when you integrate tangential acceleration with respect to time? What does the '$v$' ...
- 1,106
1
vote
1
answer
900
views
Derivative of position vs displacement with respect to time?
So i have been told that the first derivative of a position function x(t) with respect to time gives me the instantaneous velocity, but i also encountered other material online which stated that the ...
- 85
-1
votes
1
answer
1k
views
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,...
- 564
0
votes
4
answers
6k
views
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 ...
- 25
11
votes
2
answers
3k
views
Kinematic equation as infinite sum
I'm not sure exactly how to phrase this question, but here it goes:
$v=\dfrac{dx}{dt}$ therefore $x=x_0+vt$
UNLESS there's an acceleration, in which case
$a=\dfrac{dv}{dt}$ therefore $x=x_0+v_0t+\...
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
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
0
votes
1
answer
45
views
Equations of motion acceleration doubt
So i was going through some text today morning. Where it said
$$ a = \frac{vdv}{dx} $$
So they then went on to,
$$ vdv = adx \\ \implies \int vdv = \int adx$$
But,I am very certain acceleration is ...
- 23
0
votes
1
answer
2k
views
Derivation of centripetal acceleration
While reading HC Verma chapter 7 circular motion I came across a derivation which I couldnt understand. I have marked my doubt with red. I don't understand from where +dw/dt [- i sine +j cos0] came ...
- 997
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
2
votes
1
answer
125
views
Vector Derivative: General Case
From "An Introduction to Mechanics" by Kleppner & Kolenkow, SIE-2007, Chapter 1 (Vectors and Kinematics), Section 1.8 - "More about the derivative of a vector".
In this section, towards the end, ...
- 203
2
votes
0
answers
136
views
Position, velocity, acceleration, jolt, and [duplicate]
I am familiar with the fact that $\displaystyle{\frac{dx}{dt}}=v$, $\displaystyle{\frac{dv}{dt} =a}$, and $\displaystyle{\frac{da}{dt}=J}$ where $J$ denotes the 'jolt', or jerk. Are further ...
- 190
-1
votes
1
answer
762
views
Uncertainty in Range of Projectile [closed]
If we are given that a projectile is launched with velocity 10m/s at an angle of $45^\circ$ and uncertainty in angle is of $0.5^\circ$ . What is the uncertainty in the range of projectile.
The problem ...
- 53
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
2
answers
4k
views
Free falling and bouncing back
My confusion arises with free falling body.
For a free falling body the displacement ~ time graph has a kink (at the time when the body hit the ground ). at a kink point, a function is not derivable ...
- 13
0
votes
1
answer
100
views
Why trajectories approach to origin tangent to the slower direction?
I am reading non-linear dynamics from Strogartz. Suppose, I have two solutions of a non linear system: $x(t) = x_0e^{at}$ and $y(t) = y_0e^{-t}$, where $a\in \mathbb{R}$. Now it is clear that,for $a&...
- 27
2
votes
4
answers
733
views
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 ...
- 4,984
3
votes
1
answer
271
views
How is $ \frac{dv}{ dt} = a $?
I know how , in the physical sense -
$$\frac {dv}{dt} = a$$
But, even after thinking a lot, I am not able to see the fault in this -
$$\frac {dv}{dt} = \frac {d(st^{-1})}{dt}
= \frac {sd(t^{-1})}...
- 141
2
votes
3
answers
179
views
Difference between $|d{\bf r}|$ and $d|{\bf r}|$
What is the difference between $|d{\bf r}|$ and $d|{\bf r}|$ and why are both of them not always equal to each other?
My question might seem stupid to some and will probably get downvoted but I have ...
- 733
0
votes
3
answers
960
views
Acceleration derivative
I am reading Morris Kline's "Calculus" and I fail to understand this notation:
We have acceleration to which an object $r$ feet from the center of the earth (and above the earth) is subject. If we ...
- 147
2
votes
4
answers
20k
views
How to find tangential/radial/angular velocity for motion in any curve? [closed]
Is the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction? If so why?
Please try to give a different explanation ...
- 188
0
votes
1
answer
123
views
How do I set when the object isn't moving
I started studying instantaneous velocity derivatives using only now.
It may seem stupid but really I'm not sure whether that's right: I have an equation:
$$x (t) = 1.5t - 9,75t³$$
To set the time ...
- 107
0
votes
2
answers
995
views
Can we say that the instantaneous velocity of an object is the displacement in zero time?
Can we say that the instantaneous velocity of an object is the displacement in zero time?
In the image above the instantaneous velocity of the object as change in time gets closer and closer to zero ...
user66452
3
votes
9
answers
4k
views
Can velocity be an undefined quantity?
We have the image below displaying the uniform velocity by time-distance graph. At every point velocity is constant but what if distance and time both become zero as at origin in the graph is? The ...
user66452
4
votes
2
answers
18k
views
Why and when do we differentiate or integrate equations in physics? [closed]
I'm an engineering student and none of my professors ever explained why do we use derivations and/or integrations in physics. So I have this task, it goes like:
The object is moving in a positive ...
- 41
2
votes
2
answers
345
views
Determining Acceleration Based On Graph
I understand how to solve this problem, but I am unsure how to generate an equation for the graph (below). My current attempt involves using the mass provided along with the derivative of the line (...
- 123
5
votes
4
answers
5k
views
How can there be really any instantaneous velocity?
I have read about Zeno's arrow paradox that tells us there is no motion of the arrow at a particular instant of its flight. It can be inferred that there can be no velocity at any instant. Moreover we ...
user36790
3
votes
1
answer
133
views
Contradiction of a scalar product
Can anyone resolve this contradiction:
$$\vec{r}\cdot\dot{\vec{r}}=\frac{1}{2}\frac{d}{dt}\left(\vec{r}^2\right)=\frac{1}{2}\frac{d}{dt}\left(\left|\vec{r}\right|^2\right)\equiv\frac{1}{2}\frac{d}{dt}...
- 393
0
votes
2
answers
5k
views
How is the direction of the instantaneous acceleration determined?
I know from the text book that the direction of velocity at any point on the 2D path of an object is tangential to the path at that point and is in the direction of motion. But how would one determine ...
- 941
0
votes
1
answer
238
views
Why do these equations result an incorrect unit for acceleration?
Hello everyone.
Imagine an object moving around a certain point on a circular orbit. Magnitude of the velocity is constant during the motion ($|v|$). The orbit radius is $r$. (I'd better notice that ...
- 1,914
1
vote
4
answers
6k
views
When we take time derivative of a function of time, then is the result another function of time, again?
(I'll try to explain my question by one known example), for example where the velocity is a function of time v(t) then its time derivative (which is acceleration: $a=\frac {dv}{dt}$) is another ...
- 21
2
votes
7
answers
44k
views
Is acceleration $a = s/t^2$, or $a = 2s/t^2$, or something third?
I'm having trouble understanding some of the stuff regarding movement in my introductory physics class (I never thought I'd say that...)
Acceleration is defined as $ a = \frac{s}{t^2}.$
Distance can ...
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