Hi everyone,
Quick question I may just not be thinking right here but I was trying to find the acceleration, velocity, and position of a rocket as a function of time. I started with acceleration:
[itex]a =\frac{T}{m\dot{m}t}  g[/itex] where T is the Thrust, m is the initial mass, mdot is the mass flow rate, and g is gravity. This equation seems to work out with dimensional analysis and logically it seems to make sense, but maybe I'm wrong there. So from there I integrated wrt to time to get the velocity:
[itex]v = \frac{T}{\dot{m}} ln(m\dot{m}t) gt + v_0 [/itex] Here is where the problem comes in, while I'm pretty sure I did my integration right, the units don't work out properly and velocity doesn't start out at 0 either, unless you set the [itex] v_0 [/itex] term to some value. Finally I tried to get position by integrating v:
[itex]s = \frac{T}{\dot{m}^2} ((m\dot{m}t)ln(m\dot{m}t)  (m\dot{m}t))  0.5gt^2 + v_0t + s_0 [/itex] Again the units don't work out properly.
I'm just considering where the rocket goes vertical for now, no horizontal components.
What am I not seeing here? This should be fairly straight forward. Thanks in advance for any help.
