View Single Post
Feb19-12, 09:44 PM
P: 11
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.
Phys.Org News Partner Science news on
Scientists discover RNA modifications in some unexpected places
Scientists discover tropical tree microbiome in Panama
'Squid skin' metamaterials project yields vivid color display