All Questions
8 questions
9
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4
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Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant but acceleration is constant?
Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant, but rate of change of velocity is constant?
Like speed is only the magnitude, so ...
1
vote
2
answers
142
views
Average velocity showing different results
I was solving a question, in which, a particle has travelled a distance $s$, with initial velocity $0$ and constant acceleration.
So the equation of motion becomes,
$$ v = a t \tag{1} $$
and
$$ v = \...
- 56
0
votes
1
answer
48
views
In circular motion is acceleration vector and $\frac{dv}{dt}$ the same?
I was studying a book in which they have written this
$$ a = -w^{2} r \hat{e} + \frac{dv
}{dt} \ddot{e} \tag{1} \label{1}$$
Where $a$ is acceleration vector $\hat{e}$ is unit radial vector and $\ddot{...
1
vote
1
answer
94
views
Simple difference between module of velocity and time derivative of module of position [duplicate]
What is the conceptually difference between the two:
$$\frac{d|\vec{r}|}{dt}=\frac{\vec{r}\cdot\frac{d\vec{r}}{dt}}{|\vec{r}|}\neq|\dot{\vec{r}}|\equiv \bigg|\frac{d\vec{r}}{dt}\bigg|$$ ...
- 189
0
votes
0
answers
46
views
1/velocity for higher dimensions
I have a somewhat basic question. I am sorry if it trivial.
Denote the velocity by $v=\frac{dx}{dt}$ suppose that $x \in \mathbb{R}^n$ and I want to parametrize $t$ in $x$ and compute $\frac{dt}{dx}$. ...
- 103
2
votes
1
answer
267
views
Is there a difference between instantaneous speed and the magnitude of instantaneous velocity?
Consider a particle that moves around the coordinate grid. After $t$ seconds, it has the position
$$
S(t)=(\cos t, \sin t) \quad 0 \leq t \leq \pi/2 \, .
$$
The particle traces a quarter arc of ...
- 131
-1
votes
2
answers
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. ...
- 67
1
vote
3
answers
2k
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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 ...
- 341