|Jan31-13, 01:15 PM||#1|
I want to calculate how is acceleration changing if I have changing mass, but constant trust i.e. :
T = m*a
a = T / m
(I know it has to be calculus).
Then again I also wan't to be able to calculate displacement and velocities etc..
Trying to find somewhere on the internet a tutorial on equations of motion when the acceleration is varying.. but most of the time I find equations for constant-acceleration.
Do you have a good tutorial ? (don't point me to wikipedia, it is good as reference but not as tutorial)
I would like also to have some simple Exersises, so I can figure out how it is done in general.
|Jan31-13, 02:06 PM||#2|
You are on the right track. a = T/m and it takes calculus.
The derivitive of 1/m with respect to m is -1/m2
So for constant T, the derivitive of T/m with respect to m is -T/m2
The minus sign indicates that as m increases the quotient T/m decreases.
|Jan31-13, 04:14 PM||#3|
Nice.. ok now how can I calculate displacement or time taken to cross specific distans having this acceleration...
I suppose I can't use :
d = x + v*t + 1/2 a*t^2
because this is only valid for constant acceleration ?
|Feb1-13, 07:02 AM||#4|
You are correct. For a non-constant acceleration instead of computing the change in velocity by simply multiplying acceleration by time, you have to compute it by integrating acceleration over time using calculus.
Similarly, for a non-constant velocity you compute change in position by integrating velocity over time rather than simply multiplying velocity by time.
You end up with a double integral.
The first integration to compute velocity as a function of time results in:
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