MHB Difference between a(t), a(v) and a(x)

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The discussion clarifies the differences between $a(t)$, $a(v)$, and $a(x)$ in terms of acceleration. $a(t)$ represents acceleration with respect to time, defined as $a(t) = \d{v}{dt}$. In contrast, $a(v)$ and $a(x)$ are not simply derivatives of velocity or position; rather, $a(v)$ can be expressed as $a(t(v))$, indicating acceleration as a function of time related to velocity, while $a(x)$ is similarly defined as $a(t(x))$. This distinction emphasizes that acceleration can be analyzed through different variables, each providing unique insights into motion. Understanding these relationships is crucial for accurately describing dynamics in physics.
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What is the difference between $a(t)$, $a(v)$ and $a(x)$? If $a(t) = \d{v}{dt}$ then what will $a(v)$ and $a(x)$ equal to?

$a(t)$ is acceleration with change in time

$a(v)$ is acceleration with change in velocity

$a(x)$ is acceleration with change in position
 
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pcforgeek said:
What is the difference between $a(t)$, $a(v)$ and $a(x)$? If $a(t) = \d{v}{dt}$ then what will $a(v)$ and $a(x)$ equal to?

$a(t)$ is acceleration with change in time

$a(v)$ is acceleration with change in velocity

$a(x)$ is acceleration with change in position

Hi pcforgeek! ;)

I believe you already have the difference.We can indeed say that $a(t) = \d{v}{t}$, but generally $a(x) \ne \d{v}{x}$ and $a(v) \ne \d{v}{v}$.

The best I can say about $a(v)$ is that $a(v) = a(t(v))$ , where $t(v)$ is the function that says at which time we have speed $v$.
Similarly $a(x) = a(t(x))$.
 
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