hi, 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. thank you
You are on the right track. a = T/m and it takes calculus. The derivitive of 1/m with respect to m is -1/m^{2} So for constant T, the derivitive of T/m with respect to m is -T/m^{2} The minus sign indicates that as m increases the quotient T/m decreases.
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 ?
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: http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation
Conservation of momentum, mv, leads to (mv)'= m'v+ mv'= 0 (the ' indicates the derivative) if there is no external force. If there is a force, then we do not have conservartion of momentum but have (mv)'= m'v+ mv'= F.