Thrust and weight verse g force upon object

simplesimon11

Have designed a solid fuel and liqiud fueled rocket engine.
Not great in mathmatics!
Have total weight of fuel engine and power supply at 2.3 pounds

Have an engine that burns for 3.3 seconds and produces 47 pounds thrust for 2.1 seconds.

If I built a stable rocket design I need to know speed rocket will obtain and would like to know total distance such will obtain.

Asking as the way I understand things I will be placing G forces unto the whole rocket which means it will become heavier with each G! I plan on a rocket body of total weight of 5 pounds!
I have built another engine based upon this engine design that will produce same thrust for 22 seconds and its total weight is 6 .8 pounds. Decided to use smaller engine in trials.

So can any one help me with this simple problem most of you good folks do as play time calculations?
Not sure how to make sub and super script on this forum. So please excuse my abilites.

Have been using this as base to figure everything out but I am lost. Thanks guys

What I have used:
M= instantaneous mas of rocket
u= velocity of rocket
t = time
F = net force = thrust = m Veg
Veg = equivalent engine exhaust velocity=Isp Go
mf=full mass
me = empty mass
mp=mass of propellant
Isp=specific impluse

Mass of engine unfueld is 1 pound
What I came up with is this equation but unable to calculate the answers with my varibles!

Δ u = Veg In(mf/me)= Veg In MR=ISP go IN MR