All Questions
Tagged with calculus acceleration
96
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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
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2
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147
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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
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2
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884
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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
3
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answers
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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
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2
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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
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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
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3k
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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
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294
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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 ...
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285
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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
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3
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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
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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 ...
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1
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273
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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 ...
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483
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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
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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
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1
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425
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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 ...
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