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A= dv/dt

by vijay_singh
Tags: dv or dt
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vijay_singh
#1
Aug4-09, 12:02 AM
P: 28
I see in many text that a = dv/dt implies that

dv = a dt

How is that possible, can anybody please explain me. As far as i know dv/dt is a symbol for derivative of v w.r.t t and not ratio between dv and dt.
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Cyrus
#2
Aug4-09, 12:11 AM
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What you wrote is in differential form.
jgens
#3
Aug4-09, 12:19 AM
P: 1,622
Rather than offer a sub-par explanation, this thread - with input from several knowledgeable members - should answer your questions: http://www.physicsforums.com/showthread.php?t=328193

bucher
#4
Aug4-09, 12:21 AM
P: 77
A= dv/dt

dv/dt is not a symbol. It is the mathematical formula for the derivative of v with respect to t. This is how one would show any derivative of a dependent variable with respect to an independent variable.
vijay_singh
#5
Aug4-09, 09:30 AM
P: 28
Quote Quote by bucher View Post
dv/dt is not a symbol. It is the mathematical formula for the derivative of v with respect to t. This is how one would show any derivative of a dependent variable with respect to an independent variable.
And what did I say :-)
vijay_singh
#6
Aug4-09, 09:31 AM
P: 28
Quote Quote by jgens View Post
Rather than offer a sub-par explanation, this thread - with input from several knowledgeable members - should answer your questions: http://www.physicsforums.com/showthread.php?t=328193
Thanks Jgens, for pointing me to right direction.
arildno
#7
Aug4-09, 09:56 AM
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Now, WHY can we utilize at times the dv=adt formula, in particular, WHERE is it usable?

Answer:

When doing integration with the technique called substitution of variables (i.e the "inverse" of the chain rule):

Given a=dv/dt, we have, trivially:
[tex]\int_{t_{1}}^{t_{2}}adt=\int_{t_{1}}^{t_{2}}\frac{dv}{dt}dt[/tex]
But the right-hand side can, by the theorem of substitution of variables, be reformulated, giving the identity:
[tex]\int_{t_{1}}^{t_{2}}adt=\int_{v(t_{1})}^{v(t_{2})}dv=\int_{v_{1}}^{v_{2 }}dv[/tex]

Now, by IGNORING that the limits of integration actually refers to the limits of DIFFERENT variables, we "may say" that the "integrands" are equal, i.e, adt=dv!


Thus, adt=dv should, at this stage of your education, be regarded as notational garnish (or garbage, if you like!)


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