All Questions
Tagged with calculus acceleration
97
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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
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5
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148
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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
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12k
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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
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2
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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
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2
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111
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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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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
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2
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2k
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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, $a(x)$, ...
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152
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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
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2
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2k
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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
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7
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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
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3
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62
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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
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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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90
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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 ...
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431
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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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5
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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.)
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