All Questions
Tagged with calculus acceleration
97
questions
2
votes
1
answer
538
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
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
0
votes
0
answers
227
views
How to determine the distance travelled before a maximum acceleration is reached given a constant jerk?
Problem
Given:
An initial velocity and acceleration of 0.
A maximum acceleration $A$
A constant jerk $J$
How might one determine the distance $D$ traversed before the maximum acceleration $A$ is ...
- 121
-1
votes
2
answers
167
views
Problem in instantaneous acceleration and instantaneous velocity
Recently i came accross a problem that said
An object is dropped straight down from helicopter the object falls faster and faster but its acceleration decreases over time becoz of air resistance. the ...
- 13
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
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.&...
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
0
votes
3
answers
421
views
What is correct definition of tangential acceleration?
Is tangential acceleration the rate of change of magnitude of velocity
OR,
Is it simply the rate of change of velocity?
I am asking this because I am sort of confused, because there is no tangential ...
0
votes
3
answers
1k
views
How does gradient give $g$?
How is
$$g=-\nabla V$$
where $V$ is gravitational potential and $g$ is acceleration due to gravity.
I am new to calculus.
0
votes
1
answer
859
views
Convert Acceleration-Time Graph to Velocity Time Graph [closed]
I have a set of 40 readings that make up 2 seconds of simple harmonic motion of an extension spring and I would like to use these readings to come up with a graph and if possible a function that ...
- 13
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
1
answer
141
views
Differential Equation & MacLaurin Series for Newton’s Second Law
I am currently working with a differential equation, where I think I need to take the derivative of $ma$ (corrected as per comment). I am trying to write $F = ma$ as a MacLaurin series and eventually ...
- 151
0
votes
1
answer
335
views
Acceleration function of position and time
I have an acceleration function in python with position and time parameters and returns the acceleration value.
I need the end velocity at a position ,start velocity is zero.
how to calculate this ...
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
85
views
Kinematic displacement: why not represent higher order rates of change?
I understand that the equation for kinematic displacement is:
$x = v_{0x}t+\frac{1}{2}a_xt^2$
Perhaps my understanding is naive, but it seems like this leaves out higher order rates of change. Why ...
- 111
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
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
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
0
votes
1
answer
276
views
Trying to prove that the expression for the radial component of the acceleration is equal to $\mathbf v\cdot \mathbf v/r$
I am trying to prove that the normal component of acceleration of a particle undergoing a curvilinear motion is equal to
$\mathbf v\cdot \mathbf v/r$.
Here $\mathbf v$ is the velocity of the particle ...
- 529
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
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
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
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
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
0
votes
2
answers
42
views
Intuition of Distance covered when accelerating [duplicate]
When you're moving at $5$ m/s for $1$ second, you have traveled $5$ m.
When you're moving at $5$ m/s (initial velocity) and you accelerate $2$ m/s for $1$ second, you have traveled $5$ m + $1$ m (...
- 163
0
votes
0
answers
372
views
Why don't we define time derivative of acceleration? [duplicate]
When we started the study of kinematics we defined position and its change with respect to time. After that we defined time derivative of velocity which gave us acceleration.
These 3 concepts really ...
- 3,377
0
votes
1
answer
55
views
Change of variable in function
Suppose I have a function $h(\theta)$ measuring the height of a piston, with $\theta = \omega t$. I would like to know the vertical acceleration of this piston as $\omega$ changes at the point $\theta ...
- 1,356
0
votes
0
answers
94
views
Acceleration as the second derivative of displacement function
Let $x$ be displacement as a function of time $t$ and some other physical quantity $k$ such that
$ x = f(t,k) $
Now,
1) Will the acceleration $a$ be $\frac{\partial^2 x}{\partial t^2}$ or $\frac{d^...
- 23
0
votes
1
answer
174
views
calculate the time elapsed for a robot to pass certain distance with a load [closed]
For a robotics project I wanted to find the optimal gear ratio for my robot to travel 10 meters. Unfortunately. the acceleration is nonconstant, and that proved to make my life much harder. I think I ...
-1
votes
1
answer
272
views
Integration of Acceleration to Get Delta Velocity
How do you get delta velocity if you have times t1 and t2 and their velocities v1 and v2, but you only know their accelerations a1 and a2. If you integrate over accelerations a1 and a2, do you get a "...
- 1
0
votes
1
answer
95
views
Acceleration Question
I'm really confused how we have a distance formula from acceleration. I understand acceleration is the change of velocity/time, however I don't understand how you can calculate a distance based on a ...
- 71
0
votes
2
answers
990
views
Condition of acceleration when using $x=vt$
So my teacher told me that since $v = \delta x/ \delta t$, $\delta x = v • \delta t$ (naturally), and that is equal to the "area under the velocity-time graph", or displacement. This all makes sense ...
- 157
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:
$$\text{previous velocity} * \text{time} + \frac{1}{2} * \...
- 115
2
votes
1
answer
3k
views
Integrating an acceleration time graph gives you?
If I have a graph of Acceleration against time. Can I integrate this curve in order to find velocity and displacement?
0
votes
4
answers
659
views
Question about $a = v\ \mathrm dv/\mathrm dx$
Consider $\vec{v}$ Now differentiating this w.r.t time,
$$\vec{a} = d/dt( \vec{v}) = \vec{v}(d\vec{v}/dx)$$
Now this multiplication of vectors obviously makes no sense. This along with the fact that ...
- 1,096
-1
votes
1
answer
207
views
Is there any reason why acceleration should not be the first derivative of the absolute value of velocity? [closed]
I ask mainly because I am not familiar enough with newtonian mechanics and higher-level physics in general to know the repercussions of such a change, but on the simpler plane of existence, I have ...
- 1
11
votes
2
answers
3k
views
Kinematic equation as infinite sum
I'm not sure exactly how to phrase this question, but here it goes:
$v=\dfrac{dx}{dt}$ therefore $x=x_0+vt$
UNLESS there's an acceleration, in which case
$a=\dfrac{dv}{dt}$ therefore $x=x_0+v_0t+\...
5
votes
2
answers
2k
views
Why does acceleration need to be constant if integrating?
My teacher wrote the following:
Constant Acceleration
If acceleration is constant, then:
$$\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
0
votes
4
answers
262
views
Explain $\Delta x = v_0t + \tfrac{1}{2}gt^2$ please? [duplicate]
$g = \Delta v/t$, so $\Delta v = gt$. $v = v_0 + \Delta v$, so $v = v_0 + gt$. So if $\Delta x = vt$, then $\Delta x$ should be $v_0t + gt$. Why the $\tfrac{1}{2}gt^2$? I'm really confused, so this ...
- 43
-1
votes
1
answer
1k
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Calculating Potential Energy
I'm familiar with the potential energy equation, but I'm concerned with the value of 'g' in it. I know that, at sea level, earth's gravitational acceleration is 9.81 m/s/s. So I know that within the ...
- 307
0
votes
1
answer
74
views
Current Electricity
If
$$
\frac{dQ}{dt} = I
$$
and if an accelerated current produces E.M. waves (radiation), does that mean $d^2Q/dt^2$ (second derivative of a charge w.r.t. time) will give me the magnitude of the wave ...
- 3
2
votes
3
answers
1k
views
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
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,
$$\...
- 383
2
votes
2
answers
15k
views
Calculate displacement in position from knowing constant acceleration
I have recently started studying physics at school, and my teacher went over the following equation without explaining about it too much:
$$s=\upsilon_{0}t+\frac{1}{2}a t^2
$$
I have wondered, why ...
- 137
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