All Questions
Tagged with acceleration calculus
11
questions
20
votes
5
answers
132k
views
How to get distance when acceleration is not constant?
I have a background in calculus but don't really know anything about physics. Forgive me if this is a really basic question.
The equation for distance of an accelerating object with constant ...
- 1,517
24
votes
7
answers
12k
views
Zero velocity, zero acceleration?
In one dimension, the acceleration of a particle can be written as:
$$a = \frac{dv}{dt} = \frac{dv}{dx} \frac{dx}{dt} = v \frac{dv}{dx}$$
Does this equation imply that if:
$$v = 0$$
Then,
$$\...
- 383
1
vote
7
answers
281
views
I'm having trouble understanding the intuition behind why $a(x) = v\frac{\mathrm{d}v}{\mathrm{d}x}$ [duplicate]
I was shown
\begin{align}
a(x) &= \frac{\mathrm{d}v}{\mathrm{d}t}\\
&= \frac{\mathrm{d}v}{\mathrm{d}x}\underbrace{\frac{\mathrm{d}x}{\mathrm{d}t}}_{v}\\
&= v\frac{\mathrm{d}v}{\mathrm{d}x}
...
- 329
3
votes
2
answers
285
views
Motion with constant speed and constant acceleration magnitude
I was reading this and this posts. From what I gather
In 2D: Constant speed $||\dot x||=const$ and constant positive magnitude of the acceleration $||\ddot x|| = const$ imply circular motion.
In 3D: ...
- 247
1
vote
2
answers
129
views
Time derivative of unit velocity vector?
Let's say I have some parametric curve describing the evolution of a particle $\mathbf{r}(t)$. The velocity is $\mathbf{v}(t) = d\mathbf{r}/dt$ of course. I am trying to understand what the expression ...
0
votes
4
answers
658
views
Question about $a = v\ \mathrm dv/\mathrm dx$
Consider $\vec{v}$ Now differentiating this w.r.t time,
$$\vec{a} = d/dt( \vec{v}) = \vec{v}(d\vec{v}/dx)$$
Now this multiplication of vectors obviously makes no sense. This along with the fact that ...
- 1,096
2
votes
5
answers
1k
views
Acceleration and motion can be in different direction?
I'm not getting what acceleration concept is and how it relates to motion and how motion and acceleration can be in different direction? And what's behind the concept of negative and positive ...
- 31
1
vote
3
answers
12k
views
Does the SUVAT equations of motion (Kinematics) come from some differential equation?
Wikipedia says about the equations of motion that;
"If the dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics.&...
0
votes
2
answers
520
views
How do I get the velocity $v$ as a function of position $x$ from the acceleration $a$ as a function of velocity?
Suppose that a particle is moving with a non-constant acceleration on the $x$ axis of $$a(v)= Av^2+Bv+C$$ ($A$, $B$ and $C$ are constants) with an initial velocity of 0 on the x axis and an initial ...
0
votes
1
answer
248
views
How to calculate traveled distance with non-constant acceleration in time?
I know this formula $D = vt + \frac{1}{2}at^2$ for calculating the distance given initial velocity, time and acceleration. But what if my acceleration is not static, but increasing exponentially ...
- 853
0
votes
3
answers
230
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