All Questions
10 questions
9
votes
4
answers
4k
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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}$$
Where $a$ is acceleration vector $\hat{e}$ is unit radial vector and $\ddot{...
0
votes
0
answers
46
views
1/velocity for higher dimensions
I have a somewhat basic question. I am sorry if it trivial.
Denote the velocity by $v=\frac{dx}{dt}$ suppose that $x \in \mathbb{R}^n$ and I want to parametrize $t$ in $x$ and compute $\frac{dt}{dx}$. ...
- 103
2
votes
1
answer
267
views
Is there a difference between instantaneous speed and the magnitude of instantaneous velocity?
Consider a particle that moves around the coordinate grid. After $t$ seconds, it has the position
$$
S(t)=(\cos t, \sin t) \quad 0 \leq t \leq \pi/2 \, .
$$
The particle traces a quarter arc of ...
- 131
4
votes
4
answers
413
views
Suppose there is a vector $\vec v$ which is a function of time, then will $\dfrac{d}{dt}|\vec v|$ be a vector quantity or a scalar quantity?
Suppose there is a vector $\vec v$ which is a function of time, then will $\dfrac{d}{dt}|\vec v|$ be a vector quantity or a scalar quantity?
I think it should be scalar because, let's assume $\vec v=...
- 223
0
votes
3
answers
295
views
What does the first derivative of (2-norm) distance with respect to time tell us?
My basic physics' knowledge is a little rusty. My apologies in advance. I know that the first derivative of position or displacement with respect to time is the instantaneous velocity. Suppose I have ...
-1
votes
2
answers
368
views
How instantaneous speed is defined as magnitude of instant velocity? [closed]
Let $s=$distance (a variable)
we define instantaneous speed = magnitude $\left[\frac{ds}{dt}\right]$.
However instantaneous speed is also defined as magnitude of instantaneous velocity
i.e. ...
- 67
-4
votes
2
answers
5k
views
Does differentiating a distance with respect to time give velocity?
I'm just wondering if you have a distance function:
$$
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?
- 163
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