# a= dv/dt

by vijay_singh
Tags: dv or dt
 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.
 P: 4,780 What you wrote is in differential form.
 P: 1,623 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
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.
P: 28
 Quote by bucher 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 :-)
P: 28
 Quote by jgens 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.
 Sci Advisor HW Helper PF Gold P: 12,016 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: $$\int_{t_{1}}^{t_{2}}adt=\int_{t_{1}}^{t_{2}}\frac{dv}{dt}dt$$ But the right-hand side can, by the theorem of substitution of variables, be reformulated, giving the identity: $$\int_{t_{1}}^{t_{2}}adt=\int_{v(t_{1})}^{v(t_{2})}dv=\int_{v_{1}}^{v_{2 }}dv$$ 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!)