All Questions
Tagged with calculus acceleration
97
questions
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,
$$\...
- 383
20
votes
5
answers
132k
views
How to get distance when acceleration is not constant?
I have a background in calculus but don't really know anything about physics. Forgive me if this is a really basic question.
The equation for distance of an accelerating object with constant ...
- 1,517
15
votes
3
answers
4k
views
Why does solving the differential equation for circular motion lead to an illogical result?
In uniform circular motion, acceleration is expressed by the equation
$$a = \frac{v^2}{r}. $$
But this is a differential equation and solving it gets the result $$v = -\frac{r}{c+t}.$$
This doesn’t ...
- 153
12
votes
4
answers
3k
views
Integrating acceleration - wrong choice of bounds in textbooks?
I've noticed in my physics textbook (and in a lot of other popular sources), that the process of integrating non-constant acceleration to get to a velocity formula, the integrating bounds imposed on ...
- 221
11
votes
4
answers
3k
views
When the direction of a movement changes, is the object at rest at some time?
The question I asked was disputed amongst XVIIe century physicists (at least before the invention of calculus).
Reference: Spinoza, Principles of Descartes' philosophy ( Part II: Descartes' Physics, ...
user229097
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+\...
9
votes
4
answers
2k
views
Can I find the acceleration or velocity when my displacement-time graph is discontinuous?
Today, I encountered the problem where I was asked to find the velocity and acceleration from displacement-time graph but the displacement-time graph was discontinuous. So I am unable to find the ...
- 123
7
votes
6
answers
2k
views
Can acceleration depend linearly on velocity?
Is it possible that acceleration may vary linearly with velocity. Is it practically possible, if so is there a practical example of it?
By integration I was able to verify that for the above case to ...
- 121
6
votes
6
answers
1k
views
Question about derivation of kinematics equations
Apologies if this has been asked before, but I browsed the sub and couldn't find something specific.
I understand the derivation for one of the equations as follows:
\begin{gather}
\frac{dv}{dt} = a ...
- 69
5
votes
2
answers
2k
views
How does instantaneous velocity or acceleration have any other numerical value than 0? [duplicate]
Instantaneous velocity is defined as the limit of average velocity as the time interval ∆t becomes infinitesimally small. Average velocity is defined as the change in position divided by the time ...
- 163
5
votes
2
answers
2k
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Why does acceleration need to be constant if integrating?
My teacher wrote the following:
Constant Acceleration
If acceleration is constant, then:
$$\vec{v}(t) = \int_0^t \vec{a}(t')dt'\ + \vec{v_0}$$
and
$$\vec{x}(t) = \int_0^t \vec{v}(t')dt'\ + \vec{...
- 1,177
4
votes
2
answers
2k
views
Calculating Intensity/Strength of Vibration with 3DOF
I want to calculate the intensity/strength of vibration at a given location. I have measured the acceleration at this location, using an accelerometer. So my measures look for example like:
...
- 43
3
votes
4
answers
2k
views
If displacement is 0, does that mean initial velocity equals final velocity?
For instance, one of the kinematic equations is :
$$v_f^2 = v_i^2 + 2ad$$
where $v_f$ is final velocity, $v_i$ is initial velocity, $a$ is acceleration, and $d$ is displacement.
Say for instance a guy ...
- 33
3
votes
3
answers
357
views
Calculating displacement from acceleration (intuitively) [closed]
If I say acceleration of car is constant at $4\; \rm m/s^2$.
Then isn’t it that it covers $4\; \rm m$ in $1\; \rm s$ with velocity $4\; \rm m/s$.
Then in $2\; \rm s$, the velocity is $8\; \rm m/s$. ...
- 725
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
3
votes
3
answers
856
views
How do you find the final velocity when acceleration is changing between two values over some distance? [duplicate]
How do you calculate a final velocity of an object when given its initial velocity and the object is accelerating between an initial and final acceleration over some given distance?
- 287
3
votes
2
answers
230
views
Generalization of straight line motion under constant acceleration
My question is that, we all know the three equations of straight line motion under constant acceleration,
\begin{align}
x & =x_{\rm o}+v_{\rm o}\,t+\tfrac12 \mathrm a\,t^2
\tag{1d-a}\label{1d-a}\\
...
3
votes
2
answers
3k
views
Difference between Instantaneous Velocity and Acceleration?
I'm studying the Speed and Velocity chapter. But there isn't anywhere mentioned in my book about clarity for the exact difference between Instantaneous speed and Acceleration. I'm curious to know ...
- 33
3
votes
3
answers
2k
views
How do acceleration, velocity, and displacement affect/relate to eachother?
I have been wondering this since learning about position, velocity, and acceleration vs time graphs but can't put numbers/equations to it.
I know that acceleration acts to change velocity, shown by ...
- 169
3
votes
2
answers
156
views
Acceleration in terms of displacement
I am having problems understanding the derivation of acceleration in terms of displacement. The first step is fine:
$$a(x) = \frac{\mathrm dv(x)}{\mathrm dt}
= \frac{\mathrm dv(x)}{\mathrm dx} \frac{\...
- 131
2
votes
5
answers
1k
views
Acceleration and motion can be in different direction?
I'm not getting what acceleration concept is and how it relates to motion and how motion and acceleration can be in different direction? And what's behind the concept of negative and positive ...
- 31
2
votes
3
answers
1k
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Basic question about acceleration [duplicate]
Very basic question.
Please show where I'm wrong in the following reasoning.
The movement of an object in function of time could be described as
$$
x(t) = v t + x_{i}
$$
if velocity is constant.
If ...
- 129
2
votes
2
answers
15k
views
Calculate displacement in position from knowing constant acceleration
I have recently started studying physics at school, and my teacher went over the following equation without explaining about it too much:
$$s=\upsilon_{0}t+\frac{1}{2}a t^2
$$
I have wondered, why ...
- 137
2
votes
1
answer
3k
views
Integrating an acceleration time graph gives you?
If I have a graph of Acceleration against time. Can I integrate this curve in order to find velocity and displacement?
2
votes
3
answers
147
views
Query regarding instantaneous velocity and instantaneous acceleration
Suppose an object's velocity is $5 \ \text{m/s}$ at $t = 1$ seconds and $8 \ \text{m/sec}$ at $t = 2$ seconds then the acceleration here is $3 \ \text{m/sec$^2$}$ i.e at $t = 1$ seconds the ...
- 13
2
votes
1
answer
345
views
When exactly does velocity increase or decrease on an acceleration time graph? [closed]
How does the acceleration time graph show if and object is speeding up or slowing down?
Is it possible to find the answer without any deep calculations? If yes then how?
Like how can I find the ...
- 117
2
votes
1
answer
202
views
How to use a piecewise acceleration function to get a position function?
This should be a relatively easy problem but I think I am missing something somewhere. This problem consists of a object that is being thrown into the air at
$t = 4s$ at a velocity $v_0$
here is my ...
- 21
2
votes
1
answer
537
views
How to determine the minimum "Arrival Distance" given a maximum velocity, acceleration and jerk along with an initial velocity and acceleration?
Problem
Given the following:
$A$ - maximum acceleration.
$J$ - constant jerk (the rate of change of acceleration).
$v$ - initial velocity.
$a$ - initial acceleration (where, in practice, $a ∈ [-A, A]$...
- 121
1
vote
2
answers
892
views
Why is position proportional to time squared?
Now I know some of the obvious answers to this, such as if you integrate the acceleration twice, you’ll get time squared, but what I’m really looking for is more of an intuitive answer.
One of the ...
- 11
1
vote
2
answers
295
views
What is the time derivative of the linear velocity vector $\vec{v}\,(t)$?
If $\vec{v}\,(t)$ denotes linear velocity, we can then write $\vec{v}\,(t)$ as $|v(t)|\hat{v}$. My question is what is $\displaystyle\frac{d\vec{v}\,(t)}{dt}?$
The answer I have seen to this question ...
- 39
1
vote
3
answers
217
views
Why does a particle initially at rest at origin with acceleration as square of its $x$ coordinate ever move?
Consider a particle initially at rest at origin, with acceleration, $a$, such that $ a(x)=x^2$.
Since the particle is at origin, initial acceleration would be 0. It's also at rest initially. Its $x$-...
- 349
1
vote
5
answers
148
views
The value of $g$ in free fall motion on earth [closed]
When we release a heavy body from a height to earth. We get the value of $g=9.8 \ ms^{-2}$. Now, I'm confused about what it means. For example, does it mean that the body's speed increases to $9.8$ ...
- 27
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.&...
1
vote
2
answers
546
views
In the equation: $a = dv/dt$ , is $dt$ the time taken to achieve that instantaneous acceleration?
If you solve for $dt$ from $a = \frac{dv}{dt}$ , is it the time taken to to achieved that instantaneous acceleration?
$a$ : acceleration
$v$ : velocity
$t$ : time
- 87
1
vote
2
answers
111
views
Why isn't tangential acceleration just $a$?
If the tangential acceleration is $\mathrm d|v|/\mathrm dt$ then isn't it just the magnitude of the acceleration of the object because $\mathrm dv/\mathrm dt$ is acceleration?
- 139
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 ...
1
vote
2
answers
2k
views
Acceleration as a function of position and time
I know if you have an acceleration as a function of $t$, $a(t)$, to find the velocity you simply integrate $a(t)$ with respect to $t$. Moreover, if the acceleration was a function of position, $a(x)$, ...
- 33
1
vote
5
answers
152
views
Equation of distance and time
How is this equation derived?
$$r = r_0 + ut + at²/2$$
where $r_0$ is the initial position of particle and $r$ is the position of the particle after all the motion it has undergone, $a$ and $t$ ...
- 131
1
vote
2
answers
2k
views
Why is there a $\frac{1}{2}$ in the kinematic equation? [duplicate]
In a few of the kinematic equations there is a $2$ or a $0.5$ coefficient. Why is this?
For example the kinematic equation for distance is:
$$\text{previous velocity} * \text{time} + \frac{1}{2} * \...
- 115
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
1
vote
3
answers
62
views
Motion in a plane situation
There is something weird I find about the following situation. Suppose a particle has the $X$-coordinate $= 2+2t+4t²$ and $Y$-coordinate $= 4t+8t²$. So it's velocity in $X$ is $2+8t$ and velocity in $...
- 45
1
vote
2
answers
147
views
Determining how long it takes an object to reach a certain speed [closed]
Robotics related. On a linear servo driven rail one can typically set acceleration and maximum move speed. I am trying to determine the amount of seconds it takes the load to accelerate to a certain ...
- 141
1
vote
3
answers
90
views
How to deal with functions of kinematic quantities not defined in terms of time?
How do I deal with functions of kinematic quantities which are not defined with respect to time?
For instance, given acceleration as a function of velocity or displacement, how would I go about ...
- 19
1
vote
1
answer
431
views
Expressing acceleration in terms of velocity and derivative of velocity with respect to position
we know that
$$a = \dfrac{dv}{dt}$$
dividing numerator and denominator by $dx$, we get $$a=v\dfrac{dv}{dx}$$ provided that $dx$ is not equal to zero or instantaneous velocity not equal to zero
when I ...
- 882
0
votes
5
answers
1k
views
Why do kinematic equations only work with constant acceleration?
People say that the equations are derived assuming a constant acceleration. I just don't see how this is the case. (I am new to calculus.)
- 324
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
0
votes
2
answers
238
views
Why are these SUVAT equations true?
\begin{align}
v&=u+at\\
s&=ut+\frac{1}{2}at^2\\
v^2&=u^2+2as\\
s&=\frac{(v+u)t}{2}
\end{align}
I have just started with learning acceleration in school and I don't really understand ...
- 119
0
votes
2
answers
54
views
Magnitude of Acceleration Vector when Speed is Constant
If I observe a change in direction of velocity, but not in speed: What does the acceleration vector look like?
I am confused! The difference vector between two vectors of equal length A has a ...
- 123
0
votes
2
answers
68
views
Motion of free fall [duplicate]
We know that according to law of free falls object, all bodies fall with the same constant acceleration. But in distance formula ($s = \frac12 gt^2$), why the acceleration is just half?
- 25
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