All Questions
Tagged with calculus acceleration
96
questions
-1
votes
1
answer
103
views
How to Find Trajectory of Particle?
Let’s say I have a particle, and I know all the forces acting on it at every position. (Let’s say the particle is in an electric/gravitational field to simplify the mathematics involved.) Now, is ...
0
votes
1
answer
78
views
In $a = dv/dt$, is $a$ the net acceleration? [closed]
While going through the calculus approach to accelerate, we have,
$$a = dv/dt, $$
I think, here, v and a should be in the same axis,
is my process correct?
in a planar motion in two dimensions, it ...
- 1
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
-2
votes
3
answers
92
views
Why is it wrong to find centripetal acceleration using change of velocity over change of time?
This question asks to find the centripetal acceleration by giving the initial and final velocity over the change of time.
As shown, my book combined two rules to find the acceleration. I utterly ...
- 377
1
vote
3
answers
207
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 $x$-...
- 337
-1
votes
1
answer
66
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Interpretation of velocity-velocity and acceleration-acceleration curves
I am parametrizing equations of motion in the form:
$$x(t) = x_0+v_{0,x}t\\y(t) = y_0+v_{0,y}t+\frac{1}{2}at^2$$
The parametrized equation with respect to time:
$$y(x) = y_0+v_{0,y}\cdot \frac{x - x_0}...
- 135
-2
votes
2
answers
98
views
Why does $\vec{a}=\vec{\omega}\times \vec{r}$ as well as the velocity does?
Today I came in class and in one of the problems the teacher used $\vec{a}=\vec{\omega}\times \vec{r}$ which made me very confused because I don't know where it comes from, it seems pulled out of thin ...
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0
votes
0
answers
43
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Physical and Diagrammatic representation of $a$=undefined when $v$=0 according to $a$=$vdv$/$dx$
$a$=acceleration
$v$=velocity
$x$=position along x axis
$t$=time instant
My teacher derived the $a$=$v$$dv$/$dx$ formula as follows
Assume a particle at time $t$ is at $x$ position having $v$ velocity
...
- 31
0
votes
2
answers
319
views
Why tangential acceleration become 0 when the velocity is max?
I Know that tangential acceleration equal to zero when the circular motion is uniform, but why it is equal to 0 , when the velocity is max or min , because there is no relation between the value of ...
- 11
-2
votes
1
answer
94
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What is $V$ in $a$=$V$$dv$/$dx$? [duplicate]
$a$=instantaneous acceleration
$V$=instantaneous velocity
$x$=position
$dx$=small Chang in position
$a$=$dv$/$dt$
multiplying numerator and denominator by $dx$,we get
$a$=$dv$.$dx$/$dx$.$dt$
now we ...
- 161
0
votes
1
answer
41
views
Are terms tangential acceleration and normal acceleration only used for instantaneous velocity?
Are terms tangential acceleration and normal acceleration only used
for instantaneous velocity?
- 23
0
votes
2
answers
65
views
While derivating equations of motion, why do we replace $v$ as $u + at$?
I was learning about the calculus derivations of equations of motion. After the derivation of $v=u + at$, where $v =$ final velocity and $u =$ initial velocity, came the 2nd Equation of motion.
In my ...
- 1
-1
votes
2
answers
64
views
Instantanous and uniform velocity and acceleration [closed]
If the mathemical expression of instantanous velocity is $d/t$, what is the mathematical expression of uniform velocity.
If the mathematical expression of instantanous acceleration is $v/t$, what is ...
- 107
0
votes
2
answers
701
views
What is the real difference between radial and tangential acceleration?
So in my physics coursebook there are two different kinds of derivation of $\frac{dv}{dt}$ of a particle rotating in a circle. Most of you will know these, they are what is called centripetal/radial ...
1
vote
7
answers
281
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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
0
votes
2
answers
268
views
Circular motion equivalent in three dimensions [closed]
Are there equations or even a concept of circular motion/tangential acceleration/centripetal acceleration in three dimensions? Maybe something called "spherical acceleration"? or am I just ...
- 75
0
votes
1
answer
87
views
How do I reconcile these two definitions of acceleration?
How do I reconcile these two definitions of acceleration?
$$a=\frac{d\bar{v}}{dt}=(\frac{dv^k}{dt}+v^i v^j \Gamma^k_{ij})\bar{e}_k \tag{1}$$
and
$$a^k=v^{\small\beta} \nabla_{\small\beta} v^k.\tag{2}$$...
- 971
0
votes
1
answer
245
views
How to calculate traveled distance with non-constant acceleration in time?
I know this formula $D = vt + \frac{1}{2}at^2$ for calculating the distance given initial velocity, time and acceleration. But what if my acceleration is not static, but increasing exponentially ...
- 853
3
votes
2
answers
156
views
Acceleration in terms of displacement
I am having problems understanding the derivation of acceleration in terms of displacement. The first step is fine:
$$a(x) = \frac{\mathrm dv(x)}{\mathrm dt}
= \frac{\mathrm dv(x)}{\mathrm dx} \frac{\...
- 131
2
votes
1
answer
339
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
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
0
votes
2
answers
507
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
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
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.)
- 314
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 ...
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
3
votes
3
answers
848
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
0
votes
2
answers
304
views
Why isn't tangential acceleration just always 0?
This is probably a very stupid question but I can't help me.
Tangential acceleration is $\vec{a_t}=\frac{dv}{dt}\frac{\vec{v}}{v}=\frac{\vec{v} \cdot \vec{a}}{v} \frac{\vec{v}}{v}$. Since $\vec{a}$ is ...
- 15
2
votes
1
answer
200
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
0
votes
1
answer
62
views
How to determine terminal velocity with speed reduction percentage and constant acceleration?
So I'm developing this game with physics.
Every frame, the body accelerates at $+4\,\mathrm{m/s^2}$.
However, every frame, the body also sets its velocity to 90% of its original value, basically the ...
- 133
0
votes
4
answers
101
views
Body is accelerating non-uniformly (acceleration is increasing with displacement). How to calculate velocity & time?
If a body is undergoing non-uniform acceleration which is increasing with displacement (It is not necessary that is directly proportional to displacement. It may be proportional to s², 1-s³, √s etc.). ...
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
2
answers
884
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 ...
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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
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
0
votes
1
answer
112
views
Why intuitively is the tangent vector the derivative of velocity of position with respect to their modulus?
When trying to find the tangential velocity, many textbooks define the tangent direction as one of the following:
or
Intuitively, why is the tangent vector the derivative of the position with ...
- 799
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
1
vote
2
answers
294
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
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
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
0
votes
1
answer
42
views
Is such a situation realistically possible where $v$-$t$ graph is continuous but $a$-$t$ graph is not?
Taking for example $v = \cos(t-1)$ from $t \in [0,1]$ and $v = e^{t-1}$ from $t \in (1,\infty)$ and $t \ge 0$. At $t = 1$, the function shifts from cosine to exponential, but remains continuous since ...
0
votes
1
answer
273
views
Can position be derived from acceleration in practice?
We know that acceleration is the derivative of velocity, and velocity is the derivative of position. But does that mean that we can find position from acceleration in practice (as opposed to in theory ...
- 879
0
votes
1
answer
483
views
Proving that acceleration perpendicular to velocity only changes it's direction [duplicate]
In a recent class, I learned about centripetal acceleration and that if a body moves in uniform circular motion the direction of velocity continuously changes implying presence of an acceleration. My ...
- 882
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}\\
...
1
vote
1
answer
425
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
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
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
0
votes
2
answers
73
views
Confusion Unit of Acceleration
I have been reading Newtonian mechanic but I got confuse in defining the unit of acceleration that "Why is the unit of acceleration $m/s^2$"?
- 11
0
votes
3
answers
165
views
Power and work contradiction
A body is starting from rest. A force is acting on it for a short period of time. In that given time, power delivered to it at any instance $t$ is given
$$P = F \cdot v_1 = ma \cdot v_1 = mv_1^2/t,$$
...
2
votes
1
answer
518
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